Biomath Communications Supplement

Analysis and an NSFD method of a model of bacterial competition in the presence of a plasmid

2023-04-17T16:27:57+03:00

The rise of antibiotic-resistant bacteria is a major threat to public health across the world. Despite the decline in incidence of many infectious illnesses, bacterial resistance is on the increase. Antibiotics are no longer effective to treat many diseases since they have been overused for decades. In this work, we construct and examine a new mathematical model of the population dynamics of antibiotic-resistant and antibiotic-nonresistant bacteria in a chemostat, where the non-resistant bacteria are infected by a homogenous plasmid that causes them to become resistant to antibiotics. The coexistence of resistant and nonresistant bacteria is possible, despite the fact that nonresistant bacteria keep entering the system. We employ a new nonstandard finite difference (NSFD) numerical method that maintains the model's positivity and its elementary stability in order to verify the theoretical conclusion. The new NSFD method is also second-order accurate.

Higher-order modified nonstandard finite difference methods for autonomous dynamical systems

2023-04-17T16:10:32+03:00

Mathematical models in biology and medicine help to better understand and accurately predict the dynamic processes involved in complex biological systems at the molecular, cellular, and organism levels. One powerful tool for modeling these systems is the use of autonomous dynamical systems. For example, in ecology, autonomous dynamical systems arise when modeling interspecies interactions, and they describe the rates of change in the population size of each interacting component. Designed to approximate specific dynamical systems, nonstandard finite-difference (NSFD) methods preserve some of the essential structural properties of the approximated system for arbitrary step-size, avoid some of the major numerical restrictions, and improve the computational efficiency. The nonstandard discretization rules were pioneered by R. E. Mickens [1] and usually include non-local discrete representations of nonlinear terms in the right-hand side of the systems and variations in the representations of the time derivatives. Series of papers have been dedicated to the development of elementary stable nonstandard (ESN) methods and positive and elementary stable nonstandard (PESN) methods, which preserve two of the most important qualitative properties of biological models, namely unconditional positivity of all feasible trajectories and local stability of existing equilibrium points. However, they are generally only of first-order accuracy.

In this project, we extend our previous work on ESN and PESN methods to develop four new classes of modified NSFD methods that are not only elementary stable and preserve the positivity of solutions, but also have second-order accuracy [2]. The proposed modified NSFD methods use a novel modified nonstandard denominator function in the discretization of the derivative, that is dependent not only on the step-size but also on the numerical solution.

We also present a set of numerical simulations for select problems in biology that support the theoretical results and demonstrate the superior performance of the proposed new methods over other classical standard and nonstandard numerical methods.

On the analysis of hemorheological data with mathematical models

2023-06-06T14:03:17+03:00

With the development of a modern experimental base, new data on the rheological, microrheological and micromechanical properties of blood and blood cells are obtained. The aim of the study is to review the existing constitutive dependencies for describing the rheological properties of blood, used as a basis for numerical simulations of blood flow in different parts of the vascular system. The purpose of the work is to clarify the interrelation between the complexes of hemorheological and micromechanical properties of blood - erythrocyte aggregation and deformability, mechanical properties of the blood cell membrane - elasticity, surface charge and others, through the analysis of prognostic hemorheological and mathematical models and numerical simulations. The analysis of the results of the simulations and their comparison with the experimental data will help to create new specific parametric models of the main characteristics of blood cells, their rheology and micromechanics - in normal conditions and in disorders of microcirculation and blood flow in various diseases, in particular in cerebrovascular, peripheral vascular diseases and in diabetes mellitus type 2 (T2DM).

Acknowledgements. The study has been supported by the Basic Research Project KΠ-06-H57/14 from 16.11.2021 "Investigation of the hemorheological parameters, the mechanical properties of the blood cells as a basis for mathematical modeling of their role for the blood flow in cerebrovascular, peripheral vascular diseases and Diabetes mellitus type 2", funded by the Bulgarian National Science Fund.

Evaluation of the effectiveness of health countermeasures against infectious disease arrival times

2023-04-14T15:05:06+03:00

Public health measures to curb the international spread of infectious diseases include stricter quarantine and border blockades. While these measures are effective in delaying the importation of infectious diseases, they also have a significant economic impact by stopping the flow of people and goods. Arrival times of infectious diseases are often used to assess the effectiveness of quarantine. Although arrival times are highly dependent on the number of infected cases in the endemic country, direct comparisons have not yet been made. Therefore, in this study, we explicitly derive the relationship between the number of infectious cases and arrival time.

Infection behavior is stochastic, and deterministic models are not always realistic. In this study, random differential equations, which are differential equations with stochastic processes, are used to describe the infection dynamics in endemic countries. The flow of travelers from the endemic country is expressed in terms of survival time, and arrival time to each country is calculated. We also considered scenarios in which PCR kits are distributed between endemic and disease-free countries, and evaluated the impact of different distribution rates on arrival times.

Simulation results showed that increasing the distribution of PCR kits in the epidemic country was more effective in delaying arrival times than using PCR kits in quarantine in disease-free countries. Increasing the proportion of infected individuals identified for quarantine in the endemic country was also found to be more important and effective in delaying arrival time than increasing the number of PCR tests.

Dynamical analysis combined with parameters identification for a model of infection in honeybee colonies with social immunity

2023-05-16T14:24:46+03:00

Several models on honeybee population dynamics have been considered in the past decades, which explains that the growth of bee colonies is highly dependent on the availability of food and social inhibition. The phenomenon of the Colony Collapse Disorder (CCD) and its exact causes remain unclear and here we are interested on the factor social immunity.

We work with the mathematical model in [1]. The core model, consisting of four nonlinear ordinary differential equations with unknown functions: brood and nurses B, iB, N and iN represent the number of healthy brood, infected brood, healthy nurses, and infected nurses, respectively.

First, this model implements social segregation. High-risk individuals such as foragers are limited to contact only nectar-receivers, but not other vulnerable individuals (nurses and brood) inside the nest. Secondly, it includes the hygienic behavior, by which healthy nurses actively remove infected workers and brood from the colony.

We aim to study the dynamics and its long-term behavior of the proposed model, as well as to discuss the effects of crucial parameters associated with the model. In the first stage, we study the local stability of the model around each equilibrium points in dependence of the reproduction number.

In the second stage, we investigate the inverse problem of parameters identification in the model based on finite number time measurements of the population size. The conjugate gradient method with explicit Frechet derivative of the cost functional is proposed for the numerical solution of the inverse problem.

Computational results with synthetic and realistic data are performed and discussed.

In silico screening of natural compounds and discovery of novel acetylcholinesterase inhibitors

2023-05-17T16:26:00+03:00

Alzheimer's disease (AD) is a widespread neurodegenerative disease that is currently treated symptomatically by inhibiting the acetylcholinesterase (AChE) enzyme. This enzyme is responsible for breaking down the neurotransmitter acetylcholine into acetate and choline at the synaptic cleft. However, the search for more effective AChE inhibitors (AChEIs) with fewer side effects has intensified in recent years, as the number of affected people has increased dramatically.

Natural compounds (NCs) are considered safer and less toxic than synthetic drugs, and therefore, we virtually screened 150,000 NCs via molecular docking. As a result, we discovered thirty-two new molecules from twenty-three structural groups. To estimate the stability of the complexes with AChE, molecular dynamic simulations were performed. Ten compounds formed stable complexes with the enzyme, and these were experimentally tested for AChE and antioxidant activity.

Five compounds exhibited moderate AChE inhibitory activity, and three of them exhibited potent antioxidant activity. These findings suggest that these natural compounds could potentially be developed into effective and safe AChEIs for the treatment of AD, as well as potential antioxidant therapies for other neurodegenerative diseases.

The results are published and are freely accessible at: http://www.ddg-pharmfac.net/.

Predicting hereditary BRCA1/2 mutations using publicly available data

2023-05-19T16:17:39+03:00

Over the past decade, biomedical sciences have become more open towards scrutiny by the general public. Modern journals publish articles open access while increasingly many research-related institutions demand disclosure of the related data sets (e.g., via websites) for reproducibility, information exchange, and validation. Still, a certain amount of sensitive data has to be kept under restricted access because of data protection guidelines, for example, data on genetic samples containing germline variants (i.e., hereditary mutations). A further difficulty is that data on mutations can be also quite opaque wrt. its provenance. However, access not only to such data but also to the corresponding metadata is often crucial in risk assessment for inherited medical conditions.

In this contribution, we focus on the hereditary breast and ovarian cancer syndrome (HBOC) and present a novel approach to assess the combined personal/familial risk of carrying a pathogenic BRCA1/2 variant. Using a combination of the Dempster-Shafer theory [1] and interval analysis [2], we improve a model from [3] towards taking into account uncertainty about persons' ages. Because public germline samples are currently unavailable, we use combined findings from various open access publications on HBOC-related mutation probabilities as our factual basis.

While being computationally simple, our model yields results comparable to those of established, more complex models (relying on undisclosed data). Additionally, we give an outlook on the way to automate the predominantly manual process of information extraction from relevant publications using context awareness and pattern recognition. The so obtained data set could be appropriately released without violating privacy regulations.

Mathematical modeling of trace-metals precipitation in biofilms

2023-05-01T16:05:34+03:00

Biofilms are colonies of microorganisms embedded in a matrix of extracellular polymeric substances (EPS). They play major roles in many fields such as biotechnology and health [1].

Mathematical modelling is an essential tool in understanding biofilms and their interactions with the media in which they evolve and in particular with inorganic materials because it reduces experimental testing and scale up [2].

In this work, we present a mathematical model that describes the growth of a biofilm and the precipitation of trace-metals within the biofilm. In contrast to existing works in the literature (e.g. [3, 4, 5]), our model takes into consideration the occupation of the liquid phase (porosity) of the biofilm by the precipitates that form during the growth of the biofilm.

More specifically, the general formulation of this model includes:

A system of first order quasi-linear hyperbolic equations that model the biomass growth, the accumulation of precipitates, and the porosity. The source terms of the porosity and precipitation equations are formulated so that the space occupied by the precipitates and porosity remains constant over time.
A system of second order parabolic equations modeling the diffusion of biomass nutrients, cations, and anions which combine with cations to form precipitates. We introduced a novelty by considering the fact that anions can be produced both by diffusion and by the metabolism of bacteria.
A nonlinear ordinary differential equation which is the free boundary of the problem and takes into account the temporal evolution of the biofilm thickness.

The entire model is therefore a free boundary problem that can be adapted to any type of biofilm (including granules) and trace-metals. A numerical application of the model is proposed. Apart from the precipitation in metals in the biofilms, it includes the competition existing between the sulfate-reducing bacteria and the methanogens which are bacteria involved in the last phase of the methane production (methanogenesis). Our numerical simulations show that the concentration of precipitates is not uniformly distributed as suggested by experimental studies in [6]. Indeed, the model shows that precipitation occurs more at the bottom of the biofilm than it does at the surface in agreement with experiments.

Impact of demography on the dynamics of malaria

2023-05-03T16:40:39+03:00

Epidemiological models should account for the vital dynamics when the disease duration is comparable with the lifespan of affected individuals, the disease is lethal or recurring, or when we study the disease's long-term impact on the population. The authors often use ad hoc or generic population equations to describe the vital dynamics. In the talk, using a malaria model as an example, we shall show that the used population model can dramatically affect the dynamics of the disease, and therefore the selection of the latter requires extreme care.

Mathematical modelling for CTCE-9908 (a CXCR4 inhibitor) on B16 F10 melanoma cell proliferation

2023-03-24T16:31:14+02:00

Melanoma, resulting from the mutation of pigment-producing cells, namely melanocytes, is an aggressive malignancy and remains a major cause of skin cancer mortality. The alarming rise in incidence and mortality demonstrates the urgency for new treatment strategies. Melanoma cells overexpress CXC chemokine receptor 4 (CXCR4), which is a G-protein coupled receptor. CXCR4 is activated upon binding to its cognate chemokine ligand, namely CXCL12, which activates downstream signalling pathways, including the mitogen-activated protein kinase (MAPK), phosphoinositide 3-kinase/ protein kinase B (PI3K/AKT), phospholipase C (PLC) and Ras homolog gene member A (RhoA) pathway. The activation of these pathways contributes to melanoma metastasis by promoting tumour cell migration, survival, adhesion and proliferation. A known CXCR4 inhibitor, CTCE-9908 is a peptide analogue of CXCL12. CTCE-9908 contains an altered NH2-terminal sequence and competitively binds to CXCR4. By disrupting receptor phosphorylation, CTCE-9908 previously inhibited cellular responses associated with downstream signalling pathways of the CXCL12/CXCR4 axis and ultimately resulted in decreased migration, adhesion and proliferation levels in several cancers. Uncontrolled cell proliferation in cancer is promoted by impaired cell cycle regulation and deregulated cell death. Therefore, this study aimed to investigate the effects of CTCE-9908 on tumour cell proliferation in B16 F10 melanoma cells in vitro.

Crystal violet staining was used to study the effects of CTCE-9908 on CXCR4 inhibition on tumour cell proliferation and to determine the half-maximal inhibitory concentration (IC50). Crystal violet (CV) is a triphenylmethane dye that stains the cell nuclei and quantifies cell proliferation, or the cytotoxicity of chemicals, drugs, or toxins on cells. Crystal violet (CV) stains negatively charged molecules such as deoxyribonucleic acid (DNA). Therefore, this method can be used to determine cell proliferation or cell death when cells are introduced to death-inducing agents.

Data derived from CV experiments were used to construct a mathematical model on inhibition of cell proliferation as a function of time (24, 48 and 72 hours) and CTCE-9908 concentration (0-0.051 mM). However, no significant inhibition of cell proliferation was obtained at these conditions, and the CTCE-9908 concentration was therefore increased for experiments at 48 hours (0-0.51 mM). As a result, the mathematical model allows for approximating parameters outside the current dataset and predicting data for the increased CTCE-9908 concentrations at 24 and 72 hours. In addition, the mathematical model was used to predict an IC50 for CTCE-9908 on B16 F10 melanoma cells.

Overall, the mathematical model contributes to the knowledge of CTCE-9908 on inhibition of CXCR4-mediated B16 F10 melanoma cell proliferation and confirms that the compound inhibits the metastatic parameter, namely proliferation at the calculated IC50. CTCE-9908 may offer future treatment strategies in combination with other viable treatments against melanoma. The authors recommend that future research, such as in vivo studies, is necessary to substantiate the findings of this study.

Analysis of a basic mathematical model of CAR-T cell therapy for glioblastoma

2023-04-12T14:58:42+03:00

CAR-T (Chimeric Antigen Receptor T) cell therapy has been proven to be successful against leukaemias and lymphomas [1, 2]. Encouraged by positive treatment results scientists begin to test that therapy on different solid tumours, including glioblastoma - an aggressive primary brain tumour. We will focus on the presentation of a mathematical model, formulated as a system of two ordinary differential equations, describing the competition of CAR-T and glioblastoma tumour cells and taking into account their immunosuppressive capacity. The model is formulated in a general way, however, we follow [3] where the exponential tumour growth was assumed. In [3] several simulations were performed to study the interactions between the tumour and CAR-T cell population. Although the authors reported several significant results, little was said from an analytical point of view. Here we study the basic mathematical properties of the solutions including the existence and stability of steady states. In [3] one boost of CAR-T cells was considered. We show that it is not efficient, and eventually, the tumour grows. Therefore, we consider the effect of constant treatment (for simplicity) and look for the conditions guaranteeing the cure.

Mathematical model of CAR-T therapy taking into account cells targeting off-tumour antigens

2023-05-31T15:12:42+03:00

In [1] two mathematical models of CAR-T (Chimeric Antigen Receptor T) cell therapy were presented. The results of this therapy against leukaemias and lymphomas were positive [2, 3], but in the case of solid tumours, including glioblastoma the results were less optimistic [4, 5]. We will focus on the mathematical analysis of one of presented models, that takes into account CAR-T cells targeting no-tumour and off-tumour antigens. The system consist of four ordinary differential equations. In [1] only an initial dose of CAR-T cell treatment was considered. We consider two kind of treatments: a constant one (which will be modelled by a source term of CAR-T cells) and periodic one (modelled by an impulsive differential equations). Basic mathematical properties of the model will be presented as well as an asymptotic dynamics of solutions will be discussed.

Periodic treatment in a mathematical model of CAR-T cell therapy for glioblastoma

2023-04-13T13:38:43+03:00

In recent years, great progress has been made in the treatment of certain solid tumours with CAR-T (Chimeric Antigen Receptor T) cells. However, their implementation is more complicated than for non-solid tumours where this therapy has been shown to be effective (cf. [1, 2] for leukaemias and lymphomas). Encouraged by the positive results of the treatment, scientists are starting to test this therapy in various solid tumours, including glioblastoma - an aggressive primary brain tumour.

In our work, based on the mathematical model of CAR-T therapy proposed in [3], we study the results of periodic treatment regimen. We show that the model has a tumour-free periodic solution and study its stability. Using linearization and the Floquet theory we find a relationship between the portion of CAR-T cells and the period of application allowing for cure. Interestingly, the cure condition is the same as the condition guaranteeing local stability of the tumour-free steady state in the model with constant treatment.

On the construction of amiloid growth models

2023-05-30T16:21:54+03:00

Amyloid diseases are group of widespread neurodegenerative disorders such as Alzheimer's, Parkinson's, Creutzfeldt-Jakob's, Huntington's diseases, etc. They all are associated with starch-like deposits of insoluble 80 to 150 nm protein fibrils in the brain neurons causing neuronal death or deterioration of the interneuron contacts. In different diseases, the insoluble fibrils include different misfolded proteins enriched in beta-sheet structures, which is the reason reason to classify these diseases as beta-sheet diseases. The most common among the amyloid neuropathies is the Alzheimer's disease, affecting 6-10% of the population over the age above 65. The cost of their medical and social care worldwide is estimated at more than one trillion US dollars annually. Amyloid plaques in Alzheimer's disease are formed mainly by the aggregation of the amyloid beta proteins (Aβ). It is composed of 39 to 43 amino acids polypeptides originating from a larger transmembrane protein known as amyloid-beta precursor protein (APP). The shorter Aβ peptides are released by two proteases called gamma secretase and beta secretase. Since the Aβ structures are dominated by beta-sheets, they easily aggregate in the form of fibrils.

The formation of amyloid fibrils is a multi-step process, involving nucleation, elongation and maturation. This complex process can be studied both in terms of of molecular mechanism of protein interaction and kinetics of amyloid fibrils formation. In the first case, a good knowledge on the fine molecular structure of the monomeric proteins is required, whereas for studying the kinetics of fibril growth the molecular mechanism of interaction is not essential since the fibril growth can be regarded as an act of joining new particles (monomers) to a linearly growing chain.

The kinetics of formation and growth of amyloid fibrils depends on many factors such as the concentration of the reacting components, temperature, viscosity, binding energy, etc. From a practical point of view, it is important to know the growth phases details and also how the polymerization/depolymerization equilibrium can be shifted towards depolymerization, i.e. how the amyloid plaques can be dissolved.

In this work we discuss some methodological aspects of the creation and formulation of mathematical models describing amyloid fibrils growth from the point of view of reaction kinetics. We propose and study several reaction network models for the amiloid fibrillation processes in the citoplasm. Recent intensive research into the physicochemical properties of amyloid and its formation into fibrils points attention to mathematical growth models [1, 2]. In [2] the authors consider the growth of single amyloid fibrils and look for a mechanistic explanation of the process in terms of a biochemical reaction network.

Fibril is an olygomer composed by monomers, thus model [2] involves two reactants: fibril F and monomer M, and additionally an intermediate reactant C. Reacrant C is the fibril "in action", that is the fibril that at the given time instant is in the process of storing the monomer molecule (adding it to self in a compact form). We present several reaction kinetic models that upgrade models presented in [1] and [2] based on recent research in the detailed fibril growth mechanisms, see e.g. [3, 4, 5]. Our models may be useful in explaining certain particular steps of the fibril growth process and certain issues of interest (such as the lag phase). Our discussion is based on familiar case studies of biological growth models using reaction network theory, such as enzyme kinetics, logistic and Gompertz growth. The solutions of the presented models are sigmoidal functions graphically visualized using computer algebra systems [1, 2, 3, 4, 5].

The SEI epidemiological model generates natural classes of biological functions: analysis using reaction netwok theory

2023-05-16T16:14:08+03:00

The idea of the present research is to find analogies between classical epidemiological models and reaction networks used in chemical reactions in Biology. The Susceptible-Exposed-Infectious (SEI) epidemiological model (see [1], [2]) is considered in the context of the Chemical Reaction Network Theory as a two-step exponential (radioactive) decay reaction chain (Bateman chain): species S is transformed into species E, E is transformed into I, such that the first reaction step (S is transformed into E) is catalyzed by species I.

We study the temporal evolution of the masses/concentrations of the species involved assuming mass action kinetics, focusing mainly on the growth function describing the mass of species I as part of the SEI model. We are especially interested in the situation when one of the chain-links of the SEI model is much faster relative to the other one. We demonstrate that under certain conditions a SEI reaction network can be "approximated" by a single-step reaction, which is either of logistic auto-catalytic type, or, of a first-order exponential non-catalytic type. We thus show that the time evolution graph of the growing species changes its shape between a sigmoidal logistic-type and a concave first-order exponential-type, depending on the ratio of the two rate parameters involved.

This fact motivates us to propose some hints that may be useful for deciding on the choice of an appropriate class of growth functions when numerically simulating a given measurement data set resulting from biological (experimental) processes. More specifically, the modeller should first examine empirically the shape of the specific measurement data set (concavity, sigmoidality, location of the inflection point, lag time, etc.) and then decide what reaction network would better fit the given measurement set [1]-[5].

Assessing potential insights of an imperfect testing strategy: parameter estimation and practical identifiability using early COVID-19 data in India

2022-12-23T16:21:09+02:00

A deterministic model with testing of infected individuals has been proposed to investigate the potential consequences of the impact of testing strategy. The model exhibits global dynamics concerning the disease-free and a unique endemic equilibrium depending on the basic reproduction number when the recruitment of infected individuals is zero; otherwise, the model does not have a disease-free equilibrium, and disease never dies out in the community. Model parameters have been estimated using the maximum likelihood method with respect to the data of early COVID-19 outbreak in India. The practical identifiability analysis shows that the model parameters are estimated uniquely. The consequences of the testing rate for the weekly new cases of early COVID-19 data in India tell that if the testing rate is increased by 20% and 30% from its baseline value, the weekly new cases at the peak are decreased by 37.63% and 52.90%; and it also delayed the peak time by four and fourteen weeks, respectively. Similar findings are obtained for the testing efficacy that if it is increased by 12.67% from its baseline value, the weekly new cases at the peak are decreased by 59.05% and delayed the peak by 15 weeks. Therefore, a higher testing rate and efficacy reduce the disease burden by tumbling the new cases, representing a real scenario. It is also obtained that the testing rate and efficacy reduce the epidemic's severity by increasing the final size of the susceptible population. The testing rate is found more significant if testing efficacy is high. Global sensitivity analysis using partial rank correlation coefficients (PRCCs) and Latin hypercube sampling (LHS) determine the key parameters that must be targeted to worsen/contain the epidemic.

Asymptotic analysis for diffusion problems in thin periodic media

2023-03-30T15:51:47+03:00

In this talk, we shall present some homogenization results for a class of diffusion problems in thin periodic composite media, made up of two heterogeneous materials separated by imperfect interfaces. By using homogenization techniques adapted to thin periodic media and by considering different geometries for the microstructure and various forms for the functions describing the discontinuities involved in our microscopic problem, several models are derived at the macroscale [1-3]. Our setting might have applications in the analysis of a variety of filtering materials, such as soils or biological tissues, and, also, in the study of the electrical conduction or of the calcium dynamics in living tissues [4-6].

Modeling the introduction of sterilizing treatment for tuberculosis in low- and middle-income countries

2023-04-26T16:49:57+03:00

To reduce the costs of tuberculosis (TB) treatment, in many low- and middle-income countries, active TB infections are still controlled by non-sterilizing treatment that leaves the patients latently infected, i.e., they still bear the pathogenic bacterium (Kochy bacilli) in a dormant state. These patients may still develop an active TB infection if malnutrition, comorbidities, or immunosuppressive treatments weaken their immune systems. On the other hand, in countries with higher income, more expensive sterilizing treatment is offered to TB patients, leaving them pathogen-free.

In this presentation, we propose a mathematical model mimicking the introduction of sterilizing TB treatment in the presence of non-sterilizing TB treatment. Using this TB transmission model, we compare the epidemiological and economic performance of sterilizing and non-sterilizing cures in the long and short run. The proposed model presents the intuitive idea that sterilizing cure performs better in the long-term perspective. Yet, sterilizing treatment is considerably more expensive if the relative difference between the costs of the two treatments is maintained constant over a long time.

However, the relative cost of sterilizing treatment may decrease over time due to the development of new drug-producing technologies. In such a case, the sterilizing treatment may become even cheaper than the non-sterilizing treatment in the long-term perspective. Nonetheless, the introduction of sterilizing treatment may not seem appealing to the local healthcare authorities in low- and middle-income countries because their long-term budget for TB control is designed according to the costs of non-sterilizing treatment.

We intend to provide solid arguments in favor of introducing gradually the sterilizing treatment within the limits of the fixed budget initially designed for only non-sterilizing treatment. For this purpose, we formulate an optimal control problem with resource allocation between the two treatments and solve it numerically under the budget constraint of the isoperimetric type. As a result, we obtain the optimal resource allocation scheme and perform different epidemiological assessments compared to the baseline case, which consists of using only non-sterilizing treatment.

Optimal control approach for establishing Wolbachia in wild population of Aedes aegypti mosquitoes

2023-03-16T16:23:58+02:00

Replacements of wild Aedes aegypti mosquitoes with Wolbachia-infected insects are becoming more and more socially accepted for controlling and preventing arboviral diseases in various areas invaded by this vector species worldwide. The main characteristics of this environmentally friendly technique are [1, 2, 3, 4]: it reduces the vectorial capacity of female mosquitoes, shortens the vector life expectancy, and reduces the overall vectorial density. In particular, the presence of Wolbachia in the vector's cells impedes it from developing a viral load sufficient for infecting human individuals through mosquito bites.

Additionally, the maternal transmission of Wolbachia, combined with the effect of cytoplasmic incompatibility (CI), facilitates the spread of Wolbachia infection in wild Aedes aegypti populations. However, these two principal features (maternal transmission of Wolbachia and CI reproductive phenotype) are sensitive to thermal stress. The latter may cause a partial loss of Wolbachia infection, known as imperfect maternal transmission and imperfect CI.

This presentation is focused on the population dynamics model of Wolbachia invasion bearing the imperfections mentioned above. Under this setting, the goal of Wolbachia-based control of arboviral infections consists in achieving the coexistence equilibrium with a high density of Wolbachia-infected mosquitoes and a low density of wild mosquitoes. Our model can also be adapted to two major Wolbachia strains, wMel and wMelPop, which are being tested in field releases.

To ensure the evolution towards the desired coexistence equilibrium, we employ the optimal control approach to design the release strategies of Wolbachia-carrying insects. The control intervention aim is two-fold: minimizing the overall number of released Wolbachia-infected mosquitoes while reducing the total intervention time. Our numerical simulations with parameters for two Wolbachia strains will display different scenarios of the tradeoffs between these two objectives to offer alternatives for policymaking.

Pattern formation in the Holling-Tanner predator-prey model with prey-taxis

2023-04-19T14:47:09+03:00

The pioneering work on the Lotka-Volterra model gave rise to rich literature on the interaction of two or more species.

In this paper, the pattern formation in the Holling-Tanner predator-prey model with prey-taxis is investigated theoretically and numerically. We first summarise the qualitative properties of the model where a threshold for the appearance of pattern formation is specified. We construct a dynamically consistent nonstandard finite difference scheme for the proposed model. Numerical simulations are provided to support our findings.

The impact of C-terminal amidation on antimicrobial peptide behavior: insights from molecular dynamics simulations approach

2023-05-18T15:06:31+03:00

C-terminal amidation is a common modification found in wild-type antimicrobial peptides (AMPs) and is believed to increase their antimicrobial efficacy. However, the exact mechanism by which this modification works is not yet fully understood. It has been observed that C-terminal amidation changes both the net charge and helicity of the peptide and plays important roles in the mechanism of action. However, previous studies have overlooked the differences in the physicochemical properties of the carboxyl and amide moieties. U3.5 is a 17-amino-acid peptide (GVGDLIRKAVSVIKNIV-NH2) that is found in the skin of Australian toadlets (Uperoleia mjobergii). It shows amyloidogenic and antimicrobial properties and exhibits cross-α/cross-β forms in different environmental conditions. While it is still unknown whether its chameleon-like properties are linked to its antimicrobial activity, it is believed that U3.5 interacts with bacterial membrane lipids to stabilize its α-helical conformation.

This study used classical MD simulations to investigate the interaction between Uperin 3.5 peptide and negatively charged phospholipid bilayers (POPE: DOPG 3:1, DOPE: DOPG 1:1). To elucidate the interaction mechanism and efficiency, two structurally correlated variables, C-terminal amidation, and non-amidated peptide were introduced. The simulation results indicated that due to an increase in positive charge, C-terminal amidation is believed to increase the antimicrobial efficacy and amyloidogenic properties of wild-type peptides and facilitated rapid adsorption on the lipid bilayer.

Statistical model for identification of the relationship between SARS-CoV-2 prevalence and wastewater concentration with vaccination and delta variant mutation

2023-05-02T16:20:01+03:00

Robust statistical models relating wastewater to community disease prevalence still need to be developed. Therefore, this study conducted the Bayesian inference to identify the relationship between community wastewater for SARS-CoV-2 concentrations and the prevalence of SARS-CoV-2 antibodies. In addition, the dynamical survival analysis (DSA), a framework for using survival analysis methods to build approximate models of individual-level information, was applied to the compartmental model using ordinary differential equations.

Using an expanded Susceptible-Infected-Recovered (SIR) model with vaccinated and delta variant infection compartments, the longitudinal estimates of the disease prevalence were obtained and compared with the wastewater concentrations using a generalized linear model. The Bayesian Markov Chain Monte Carlo (MCMC) method was utilized to estimate model parameters. The model analysis revealed significant temporal differences in epidemic peaks. The results showed that in some areas, the average incidence rate based on serological sampling was 50% higher than the health department rate based on convenience sampling. In the generalized linear model, a one copy per ml-unit increase in weekly average wastewater concentration of SARS-CoV-2 corresponded to an average increase of 1-1.3 cases of SARS-CoV-2 infection per 100,000 residents.

The analysis indicates that wastewater may provide robust estimates of community spread of infection, in line with the modeled prevalence estimates obtained from stratified randomized sampling, and is therefore superior to publicly available health data. In addition, the analysis also identified that vaccination might reduce the prevalence and delta variant mutation affected significantly, increasing the infection.

PreDQ - a software tool for peptide binding prediction to HLA-DQ2 and/or HLA-DQ8

2023-05-19T16:00:30+03:00

Here, we describe a software tool, named preDQ, for peptide binding prediction to HLA-DQ2 and HLA-DQ8 proteins specially designed and developed for the European Food Safety Authority. The tool is able to identify peptides binding to HLA-DQ2 and/or HLA-DQ8 proteins and to predict their binding affinities. The tool will be used to assess the risk of novel proteins to cause celiac disease.

Predictions made by preDQ are based on five robust models and the risk assessment is reported by five outputs. The models are developed using datasets of known peptides binding and non-binding to HLA-DQ2 and HLA-DQ8 proteins. The datasets are compiled from the literature and curated. Ligand-based and structure-based methods are used in the development of the computational models. The models are validated by internal cross-validation procedures and by external test sets. Only the best performing models are selected and included in preDQ.

preDQ is a comprehensive, user friendly and reliable tool for assessing the binding affinity of peptides to HLA-DQ2 and HLA-DQ8 and the capacity of the origin proteins to cause celiac disease.

In silico immunogenicity prediction of viral proteins

2023-05-17T16:29:44+03:00

Infectious diseases are primarily caused by viral proteins, making prevention crucial for effective disease control. Vaccines can help protect against many infectious diseases and reduce their spread. The first step in the modern vaccine design and development is the application of bioinformatics tools and computational techniques to identify potential vaccine targets, usually proteins. The identification of protective immunogens is the most important and vigorous initial step in the long-lasting and expensive process of vaccine design and development.

This study aims to derive machine learning models for immunogenicity prediction of viral proteins in order to update the VaxiJen server which was developed ten years ago in our lab. The study has three main phases: data collection and database creation, implementation of machine learning algorithms to find the best prediction models, update the VaxiJen webserver.

A dataset of viral immunogens acting as protective antigens in humans was created, based on exhaustive literature searches and validated sources such as PubMed, UniProt, NCBI, IEDB, and ClinicalTrials.gov. This dataset was implemented in a database, which includes information for 1782 viral antigens, T- and B-cell epitopes, on-going and completed clinical trials with viral immunogens from 31 viruses.

To create a negative set of non-immunogenic proteins from the same viral species, the immunogenicity of the proteins from the proteomes of each virus in the dataset was assessed using the VaxiJen 2.0 webserver. This resulted in a dataset of 468 non-immunogenic proteins. The dataset of viral immunogens and non-immunogens was divided into training and test sets. The primary structures of proteins were encoded by E-descriptors and transformed into uniform vectors by auto- and cross-covariance (ACC) calculations. Various machine learning algorithms were applied to the training set to derive models using the Weka software. The derived models were then validated using the test set. The best predictive performance was observed with models derived from Xgboost (accuracy 89.85%), Random Forest (accuracy 87.15%), and Multilayer perceptron algorithms (accuracy 89.5%). The gain/ratio algorithm was used for attribute selection, resulting in a reduction in the number of attributes from 125 to 108 and an approximately 2% increase in the specificity of the selected algorithms. The last step to be fulfilled is to update the VaxiJen webserver.

Overall, this study provides an updated machine learning-based approach to predict the immunogenicity of viral proteins, which can aid in the development of effective vaccines.

Response surface designs and R package based modelling for predictive capabilities, sensitivity and validation of model for improving the bacterial growth, laccase production, and textile dye decolorization alongside a detoxification study

2023-03-22T16:19:51+02:00

The thermophilic bacterium, Bacillus licheniformis U1 is used for the optimization of bacterial growth (R1), laccase production (R2) and synthetic disperse blue DBR textile dye decolorization (R3) in the present study. Preliminary optimization has been performed by one variable at time (OVAT) approach using four media components viz., dye concentration, copper sulphate concentration, pH, and inoculum size. Based on OVAT result further statistical optimization of R1, R2 and R3 performed by Box–Behnken design (BBD) using response surface methodology (RSM) in DOE Design-Expert (Stat-Ease) and R software with R Commander package. The total 29 experimental runs conducted in the experimental design study towards the construction of a quadratic model. The model indicated that dye concentration 110 ppm, copper sulphate 0.2 mM, pH 7.5 and inoculum size 6% v/v were found to be optimum to maximize the laccase production and bacterial growth. Whereas, maximum dye decolorization achieved in media containing dye concentration 110 ppm, copper sulphate 0.6 mM, pH 6 and inoculum size 6% v/v. R package predicted R2 of R1, R2 and R3 were 0.9917, 0.9831 and 0.9703 respectively; likened to DOE predicted R2 of R1, R2, and R3 were 0.9893, 0.9822 and 0.8442 respectively. The values obtained by R software were more precise, reliable and reproducible, compared to the DOE model. The laccase production was 1.80 fold increased, and 2.24 fold enhancements in dye decolorization were achieved using optimized medium than initial experiments. Moreover, the laccase-treated sample demonstrated the less cytotoxic effect on L132 and MCF-7 cell lines compared to untreated sample using MTT assay. Higher cell viability and lower cytotoxicity observed in a laccase-treated sample suggest the impending application of bacterial laccase in the reduction of toxicity of dye to design rapid biodegradation process.

In the present research, DOE and R package compared mainly for modelling perspective. All three responses i.e. R1, R2 and R3 were checked using DOE and R package for predictive capabilities, Sensitivity and Validation of model. ANOVA and regression analysis for all three responses were superior in R package. Similarly, the predictive values of R1, R2, and R3 by R software are more suitable and justifiable than the predictive responses values of DOE. In contrast to DOE data, R package data showed the lower standard error of the regression line which represents a quick approximation of 95% prediction interval. To the best of our knowledge, there are no reports on the use of statistical design of R package for optimization of three responses simultaneously. We also emphasized R software package's sensitivity analysis and its usefulness in the optimization process through the validation approach.

This study aims to optimize the medium composition mainly required for growth of isolate, the laccase production and dye decolorization by a Bacillus licheniformis U1 strain using R open source software with R Commander (Rcmdr) package.

About sterile females contamination and residual fertility in a mosquito control program using the Sterile Insect Technique. Impact on Dengue control.

2023-05-02T16:27:22+03:00

The Sterile Insect Technique SIT is a technique to control vectors of diseases by releasing sterile males. However, after the ionization/sterilization process, sterile males are never 100% sterile such that there is a small percentage, ε, of sperms or individuals that remain fertile [1]. Sex-separation is also a complex process, such that females eggs or pupae can contaminate the males buckets, and, then, be sterilized and released. Since only females are vectors, this could be problematic when an arthropod virus, like DENV, is circulating [2]. Both issues always occurring simultaneously in SIT programs, it is important to take them into account in SIT models and to derive thresholds and/or upper bounds.

To this aim, we develop and study an entomological-epidemiological model that includes releases of sterile insects, residual fertility, and mechanical control, i.e. the removal of breeding sites. We provide numerical simulations when DENV is circulating, like in La Réunion [3]. This work is an extension of [2].

About sterile insect control strategies in a two patches system

2023-05-15T14:58:27+03:00

Sterile Insect Technique is an autocidal method to control Vector of diseases and crop pest. It consists of releasing males sterilized by ionization, in a targeted area, that will mate with the wild females, resulting in a reduce, eventually a local elimination, of the wild population. However, migration of wild insects, from a non-targeted area, can be problematic and reduce the efficiency of SIT [1]. The control strategies should be adapted to take this issue into account. We consider a two patches system, where Patch 1 is the targeted area linked to another area, Patch 2, that needs not to be controlled. Wild and sterile insects can circulate between the two Patches, so that different issues have to be solved. Is it possible to find one or several strategies, and among them an optimal strategy, to reach elimination in patch 1? Should we control both patches? Using results related to monotone cooperative systems [2] and also tools from optimal control theory, we will show some theoretical responses [3]. We will also illustrate the theoretical results with numerical simulations and discuss the extension of our results.

Construction of a new infectious disease model using the time delay

2023-05-25T15:16:15+03:00

In this research, we developed a novel approach to construct a stochastic epidemic model based on the compartment of the SEIR model. This model is considered more realistic than the SIR model because it takes into account that an individual who has just been infected with the disease does not immediately transmit the disease to another individual. When it takes a longer time for an infected person to spread the disease to others, we constructed the infectious disease model that reflects this time interval as a time delay. In general, a time delay means that an infected person may not spread the disease to others for a certain period of time, rather than immediately spreading it to others after being infected. When we don't take into account the time delay in the epidemic model, the infected person immediately spreads the disease to others, so the predicted rate of spread can be excessively high. However, with the time delay considered, the infected may not spread the disease to others for a certain period of time, so the predicted rate of spread may be more realistic.

We considered a time delay distribution that estimates how long each infected person is not able to transmit the disease to another person. We performed the Bayesian method to estimate the epidemic model with time delay and applied it to the COVID-19 data in Seoul, Korea in 2020. The time delay-considered model showed a more accurate and explainable prediction for real disease spread data, especially for highly contagious diseases or when there are high numbers of infections.

A two-stage SEIRS reinfection model with multiple endemic equilibria

2023-03-17T16:34:38+02:00

Since the introduction of SIR model by Kermack and McKendrick in 1927, compartmental models have been massively studied and successfully applied to various epidemic processes including characteristics such as quarantine, vaccination, variants, cross-immunity. Recently, a particular attention has been paid to reinfection models in epidemiology. To cite a few, threshold conditions for infection, reinfection and endemicity of various SIRS models are studied in [1], bifurcation analysis for a SIRI model presenting different contact rates for infection and reinfection in [2], and models counting reinfections in [3], [4].

Nevertheless, in most studies on reinfection, the infection and reinfection processes are assumed to behave essentially in the same way, which is quite limitative. With the aim of understanding the effects induced by differences between the stage of primo-infection and further reinfections, we introduce here an 8-dimensional two-stage SEIRS reinfection model in which the parameters characteristic of the disease dynamics are different for the primo-infection and for the following reinfections.

The value of the basic reproduction number R₀ of the model around the (unique) disease-free equilibrium is first derived, and the existence of up to two and three endemic equilibria, respectively in the cases R₀ <= 1 and R₀ > 1, is theoretically established under appropriate conditions on the system parameters. Finally, numerical testing and simulations are achieved, which in particular exhibit bistability in the cases when multiple endemic equilibria arise.

Upscaling a mixed-culture biofilm model in homogeneous porous media via multiscale asymptotics approach

2023-05-01T16:11:03+03:00

A macroscopic model for biofilm growth in a homogeneous porous medium is constructed by upscaling the one-dimensional Wanner-Gujer multispecies biofilm model. The flow through the porous medium is assumed in a laminar and convection-dominated regime. The formal multiscale asymptotics method is applied to the mesoscale coupled system of elliptic-hyperbolic equations, which is a practical tool for determining the effective extent of various biofilm processes at the field scale. The mesoscopic biofilm model is composed mainly of a dual- species biofilm subject to growth and loss due to single substrate consumption and detachment, respectively.

The constructed model is a basic skeleton and the upscaling method is flexible to consider any number of bacteria species, and can be extended to various biofilm processes and kinetics (e.g., multiple substrates consumption, metals sorption and precipitation). The upscaling procedures end up with a stiff system of hyperbolic equations that are solved numerically. An original numerical code has been implemented on the MATLAB platform, based on the Uniformly accurate central scheme of order 2 (UCS2). To prove model consistency and highlight the main novelty of the work as compared to existing models, different simulation scenarios have been investigated by varying the following parameters: attachment velocity, detachment coefficient, and fluid flow rate.

The mixed-culture biofilm assumption was found to significantly affect the overall reactor performance, and the model outputs qualitatively agree with the physical expectations.

Distributional solutions of nonlinear diffusion equations with a moving Dirac source term

2023-05-17T16:15:41+03:00

We focus on the study of singular solutions of nonlinear diffusion equations, specifically the fast diffusion and porous medium equations. Building on work on the existence of asymptotically radially symmetric solutions by Fila, Takahashi, and Yanagida, we focus on their uniqueness and the equation they satisfy in the sense of distributions. This equation involves a moving Dirac source term, which is also found in parabolic systems used in various biological applications.

Marek Fila, a supervisor, friend, and co-author of this paper, passed away in April 2023. In his memory, the second author has decided to publish the research, as this work with his valuable impact was finished before his passing.

How much precision is not enough in the computer molecular simulations?

2023-05-30T13:28:01+03:00

Computer simulations are a basic and often the only available instrument, when studying the complex phenomena of molecular interactions and molecules formation in contemporary nano-scale biological sciences. Modern simulations incorporate complicated underlying mathematics, extraordinarily large numbers of engaged numerical values, extremely small time steps and really huge numbers of iterations. Besides, the systems under simulation are chaotic by nature.

These circumstances lead to an increasing necessity to reconsider the impact of computational precision on the simulation accuracy, particularly when the behavior of individual molecules and/or atoms is in the focus of attention. This is especially true in the cases of widely adopted simulation software packages, where the pursuit of performance gain and the robust statistical indicators, used to assess the validity of the result, as a rule, neglect the above impact. The explanation for such an attitude comes from the theoretical considerations about the so-called "computed chaos". It is assumed that distinct trajectories produced by running the same simulation on the same setup, but with different computational precisions are equally valid as long as they belong to the attractor of the simulated system.

This paper presents a thorough experimental study on whether neglecting the computational precision is appropriate in some special and important cases such as very long-term simulations or simulations of non-equilibrium processes. A well known molecular simulations software package has undergone a significant replacement of its standard floating-point arithmetic with an originally developed special one - a combination of infinite precision operations inside the computationally intensive kernels and specific rounding schemes outside them.

The results, obtained by run-time monitoring of the floating-point performance and posterior trajectory analysis, show cases of dramatic impact of precision on the final simulation outcome.

Optimal coefficient restoration for COVID-19 epidemic modelling

2023-05-16T14:19:06+03:00

A mathematical deterministic compartment SIR-type model is utilized to investigate the impact of COVID-19. This model is deemed appropriate since it accounts for the non-permanent immunity of the virus after infection. It is also realistic because it considers the nonlinear incidence rate and the delayed transmission dynamics [1]. The model poses a coefficient identification inverse problem, which involves reconstructing the transmission and recovery rates. These rates are crucial for medical professionals and policymakers to make informed decisions regarding the management and mitigation of the virus.

To further elaborate, the basic models assume that individuals move from the susceptible to the infected compartment and then to the recovered compartment, and once recovered, they have permanent immunity. However, the SIR-type model accounts for the fact that COVID-19 may not confer permanent immunity after recovery, making it a more appropriate model for this virus.

The identification of the transmission and recovery rates is a challenging problem that requires the use of mathematical tools such as inverse problems [2]. This process involves estimating the unknown parameters of a model from observed data, in this case, the number of confirmed cases and recoveries. Accurately identifying these rates is essential for policymakers to make informed decisions on implementing measures to slow the spread of the virus and to allocate resources such as hospital beds and medical supplies. It also aids in the development and evaluation of effective treatments and vaccines.

The task of solving the inverse problem in this study is transformed into a minimization problem, which is tackled by finding the solution that yields the smallest squared error [3]. Once the values of the parameters are obtained, it is conducted an identifiability analysis to ensure that the estimated values are reasonable and reliable [4]. To validate the findings of the study, the results are compared with those of previous studies, using real data collected from Bulgaria. The comparison involves evaluating the consistency and accuracy of the estimated parameter values, as well as assessing the model's ability to predict the behavior of the COVID-19 epidemics.

Genome variation analysis and strategic clustering to sub-lineage of double mutant strain B.1.617 of SARS-CoV-2

2023-03-22T16:24:17+02:00

SARS-CoV-2 is an RNA coronavirus responsible for Acute Respiratory Syndrome (COVID-19). In January 2021, the re-occurrence of COVID-19 infection was at its peak, considered the second wave of epidemics across the world. In the initial stage, it was considered a double mutant strain due to two significant mutations observed in their Spike protein (E484Q and L452R). Although it was first detected in India, later on it was spread to several countries of Asia, Europe and other continents, causing high fatality due to this evolved strain. In the present study, we investigated the spreading of B.1.617 strain worldwide through 822 genome sequences submitted in GISAID on 21 April 2021. Submitted sequence data were extracted and uploaded to AnCovid19 Database (http://covid19.vnsguhpc.co.in/) for analysis. AnCovid19 was developed during study in Drupal 7.78. All genome sequences were analyzed for variations in genome sequences based on their effects due to changes in nucleotides. At Allele frequency 0.05, there were a total of 47 variations in ORF1ab, 22 in Spike protein gene, 6 variations in N gene, 5 in ORF8 and M gene, four mutations in Orf7a, and one nucleotide substitution observed for ORF3a, ORF6 and ORF7b gene. The clustering for similar mutations mentioned B.1.617 sub-lineages.

The outcome of this study established relative occurrence and spread worldwide. The study's finding represented that "double mutant" strain is not only spread through traveling but it is also observed to evolve naturally with different mutations observed in B.1.617 lineage. The information extracted from the study helps to understand viral evolution and genome variations of B.1.617 lineage. The results support the need of separating B.1.617 into sub-lineages.

The results describe that B.1.617 was not spread through India to other countries but eventually observed as a sub-lineage of B.1.617.1, B.1.617.2 and B.1.617.3. The variations E154K, E484Q, L452R, P681R and Q1071H were observed in most samples with allele frequency beyond 0.85. These variations might be responsible for several cases during the wave of COVID-19 infections. The recent submissions to NCBI GenBank database and GISAID EpiFlu Database will elucidate more variations belonging to B.1.617 and its sub-lineages. The resulting continuous tracking of such variations will generate a complete picture of epidemiology and transmission of SARS-CoV-2 during the second wave of COVID-19 worldwide.

Spatial cumulant models enable spatially informed treatment strategies in theoretical cancer systems

2023-05-31T15:38:42+03:00

Cancer cells can interact with each other by, for example, exchanging signalling molecules and competing for resources such as space and nutrients. Such cell-cell interactions have been identified as factors that drive eco-evolutionary dynamics of cancer cell populations. Consequently, these interactions have been proposed as treatment targets, where the general premise is that treatments can perturb cell-cell interactions and, by extension, disease trajectories.

We recently identified a need to formulate cancer cell population models that include cell-cell interactions and (1) are mathematically tractable (analytical), (2) are spatio-temporally resolved, and (3) maintain cell discreteness. In this presentation, I describe an approach to achieve (1-3) using spatial cumulant models (SCMs). SCMs are spatially resolved population models that are translated from a specific family of individual-based models, namely spatio-temporal point processes (STPPs).

Following a mathematical manipulation that involves a perturbation expansion around mean-field equations, SCMs approximate two STPP-generated summary statistics: first-order spatial cumulants (densities) and second-order spatial cumulants (spatial covariances). We exemplify how SCMs can be used in mathematical oncology by modelling theoretical cancer cell populations comprising interacting growth factor-producing and non-producing cells.

Our results demonstrate that SCMs can capture STPP-generated population density dynamics, even when mean-field population models (MFPMs), fail to do so. From both MFPM and SCM equations, we derive treatment-induced death rates required to achieve non-growing cell populations. When testing these treatment strategies in STPP-generated cell populations, our results demonstrate that SCM-informed strategies outperform MFPM-informed strategies in terms of inhibiting population growths. We thus demonstrate that SCMs provide a new framework in which to study localised cell-cell interactions, and can be used to describe and perturb STPP-generated cell population dynamics.

We anticipate that the opportunity to analytically derive spatially informed cancer treatment strategies, as enabled via SCMs, will inspire new theoretical and applied mathematical biology research.

Ultrasound experimental model for knee joint intra-articular movements

2023-05-19T16:12:05+03:00

Over 65% of the problems that occur in the human musculoskeletal system are of joint origin, and in some specific categories of work, including sports, it is significantly higher. The purpose of the present study was to develop an ultrasound experimental model for studying of the intra-articular femur-tibia displacements depending on the different vertical extra loads - 2, 5, 10, 15, 17 and 20 kg, applied on 17 healthy participants (7 men, 10 women).

The changes in millimeters of the distances between the femur and tibia were measured with ultrasound portable device at lower limbs straight pose near the iliotibial knee band. With increasing extraloads a decrease in femur-tibia distance was obtained. Quantitative data will help to create a mathematical model for the mechanical effects during deformation of the knee joint capsule, as well as to prepare quantitative method with software program for automatic calculation of femur-tibia kinematics from ultrasound images.

Such results are measured for the first time (in our opinion) and will be the basis for: (i) determination of the change of the contact area between the femur and the tibia under different axial loads; (ii) creation of a analytical model for evaluation of the deformation of the cartilage tissue from the contact area between the femur and the tibia under used axial loads; (iii) modeling the interaction between cartilage deformation and interstitial fluid flow from the cartilage into the joint cavity under loading.

Identification and analysis of cell-specific expressed genetic variants from scRNA-seq data

2023-05-15T15:12:09+03:00

Low cellular frequency variants may indicate pre- or early-somatic clonality in cancer and normal tissues, or cell-specific RNA variance. Currently, most genetic variation is analyzed from bulk sequencing datasets, where low cellular frequency variants are difficult to distinguish from artifacts.

To address challenges posed by low frequency variation events, we have developed a computational framework for identification and analysis of Single Cell-specific Expressed Single Nucleotide Variants (sceSNVs) from single cell RNA-sequencing (scRNA-seq) data. Central for the framework is our new tool SCExecute, which enables the execution of various software designed for bulk sequencing data on barcode-stratified, extracted on-the-fly, single-cell alignments. Applying SCExecute in conjunction with tools for analysis of bulk sequencing data, we explored, for the first-time, expressed genetic variation at cell-level across 28 publicly available cancer and normal datasets, including prostate cancer, non-small cell lung carcinoma, cholangiocarcinoma, neuroblastoma, normal fetal adrenal and normal embryo. This analysis identified over 100,000 previously unreported expressed SNVs, including somatic mutations and RNA-originating variance, such as posttranscriptional modifications and locus-specific transcriptional infidelity. Our analysis shows that over 70% of these variants cannot be identified with the current bulk-based variant callers. Furthermore, approximately 10% of these novel variants show preferential expression in particular cell clusters and pseudo-time stages. Single-cell RNA e-QTL (scReQTL) analysis revealed that the expression of such sceSNVs correlates with increased expression of their harboring gene. Moreover, differential gene expression analysis between cells expressing these sceSNVs and the neighborhood cells expressing the reference allele, showed deregulation of functional gene-networks of the SNV-harboring gene. Asymmetrically expressed sceSNVs across multiple samples are enriched in genes participating in DNA-repair, replication, and cell cycle pathways. We exemplify our analyses with a novel missense substitution - 6:26104128_G>T, expressed in a gene encoding one of the core histones (HIST1H4C^V61F). We demonstrate that HIST1H4C^V61F is correlated to high expression of HIST1H4C and deregulation of the HIST1H4C-related gene network, the observation being more pronounced in neurons, across multiple cancer samples.

Our findings suggest that there is an unappreciated repertoire of cell-level expressed nucleotide variation, possibly recurrent and common across samples, that participates in transcriptome function and dynamics in both cancer and normal cells. Their appearance and, for some, relationship to certain gene-sets and cell types, suggests novel mechanisms and function for the expressed genetic variation, including in cancer progression and cell fate.

A stochastic model of seasonal savanna

2023-05-31T15:35:44+03:00

Savannas are mixed forest-grassland ecosystems that cover around 20\% of the Earth's surface. They occur in areas with a distinct dry season and a rainy season. In understanding the complex dynamics of savannas, a major concern is how do trees and grasses coexist without one dominating the other? Random fires are believed to be key. From a mathematical point of view, most savanna modeling attempts in the literature do not consider a stochastic approach to fire occurrence, and the occurrence of seasons in deterministic models is often analyzed only numerically [1].

We propose a stochastic savanna model [2], which is formally a hybrid process described by piecewise-deterministic Markov processes [3] reflecting repeated switching between two seasons. Such a description requires an additional time variable to track the length of stay in the current season, leading to time-homogeneous Markov processes. We examine the time averages of their distributions and give sufficient conditions for their convergence. Although we focus on the savanna dynamics model as an example, we present a general theory that can be used for other formally similar models or in situations where there are more than two seasons.

Adaptive strategies destabilise the rock-paper-scissors game but increase the eco-evolutionary performance

2023-05-03T14:22:06+03:00

The rock-paper-scissors (RPS) game is a classic model used in evolutionary game theory to explore the dynamics of how multiple strategies interact and evolve over time. The classic RPS game assumes a fixed benefit and cost for each strategy when its player interacts with another player of a specific strategy, while an evolutionary RPS game considers the dynamics of three populations whose fitnesses are influenced by the net payoff of each particular strategy. This may not accurately reflect the complexity of real-world scenarios. In this study, we introduce an adaptive evolutionary game (AEG) that captures simultaneously both the trait-mediated population dynamics, and the adaptive dynamics of traits, with the traits determining the benefits and costs of the payoff matrix in the RPS game through particular kernel functions. We investigate how strategies change through the trait evolution and how such adaptive changes can affect the population performance of each strategy and the presence and stability of Nash equilibrium.

Our study reveals several key findings regarding the adaptive evolutionary RPS game. Firstly, the AEG reaches a steady state (asymptotic phase) more quickly than the evolutionary RPS game, in terms of population dynamics. Additionally, the stable coexistence of all strategies in the evolutionary RPS game is easily destabilised if allowed even small mutation rates in the AEG. We also show that adaptive strategies can enhance the population performance of the RPS game, as measured by average population densities at the steady state. Adaptive dynamics of gaming strategies exhibit diverse attractors in the trait space that depend both on the initial population densities and initial trait values, as well as parameters. Finally, the evolutionary attractors (i.e., the type of games) emerged in the AEG typically experience greater benefits than costs.

These findings, thus, highlight the effect of adaptive strategies in the RPS game that destabilises the eco-evolutionary dynamics while increases the performance of each strategy.

Self-organization or disorder phenomena in biology

2023-05-02T16:09:57+03:00

I am going to show, that the blow-ups of solutions, that usually are treated as something "very bad", can in fact describe some self-organization phenomena, "positive" (like healing) or "negative" (like society polarization). Mathematically it is the theory of integro-differential equations (kinetic-type equations) that is applied to processes in Biology - e.g. swarm formation - [1, 2] or DNA denaturation - [3], Medicine - tendon healing process - [4]. The relationships with classical PDEs models are discussed - see [5, 6].

The hybrid Gompertz distribution - derivation, characterization and estimation (a reaction network treatment)

2023-03-30T16:00:02+03:00

Using the tools of reaction network theory, we show how the well-known Gompertz probability distribution can be generalized to a new distribution - the hybrid Gompertz distribution. We characterize the hybrid Gompertz distribution using a combination of analytical and numerical methods, and compare it graphically to the standard Gompertz distribution. Selected probabilistic properties of the hybrid Gompertz distribution are presented and possible approaches to its estimation are investigated.

Acknowledgments. The work of Meglena Lazarova is supported by the Bulgarian National Science Fund under Project KP-06-M62/1 "Numerical deterministic, stochastic, machine and deep learning methods with applications in computational, quantitative, algorithmic finance, biomathematics, ecology and algebra" from 2022.

Modeling the control of breathing using a Boolean framework

2023-05-18T14:59:26+03:00

Breathing is controlled by a neural network located in the brainstem. This network is essential for supporting a wide range of activities (for example, sleep, exercise and vocalization as well as heart function). The mechanisms for generating and controlling breathing have been studied for over 30 years but they are still not well understood.

We recently developed a framework for studying neural networks based on Boolean representation. Our framework enabled us to predict the behavior of neural networks based on properties of neurons (e.g. existence of memory, threshold, and self-excitation) without relying on specific parameter values. We used our innovative framework to design a network that mimics many features seen in the respiratory neural network. It provides, for the first time, a good understanding of the way inspiration and expiration times can be controlled selectively at the level of the neural circuitry. Importantly, the Boolean neural networks within our framework can be easily scaled to represent breathing rates of different species.

On reliable numerical methods for some real-life differential equation models with singularities

2023-05-05T16:21:11+03:00

The Finite Difference Method (FDM) and the Finite Element Method (FEM) are among the most used techniques for numerical solutions of ordinary and partial differential equations. Of paramount importance is the construction of FDM and FEM that are reliable in that they permit to gain useful insight on the solutions of the continuous differential equations being studied. For boundary value problems for partial differential equations with domain-singularities such as corners, vertices and edges, there has been considerable efforts to construct innovative FEMs in which the optimal rate of convergence, with error estimates, is restored. To the convergence of a numerical method, the Nonstandard Finite Difference (NSFD) method created by R Mickens in the late eighties brings a further level of reliability of a numerical scheme, namely that it should be dynamically consistent with respect to the involved continuous differential equation [1]. The FEM or its variants and the NSFD method are abundantly used in Biosciences, the focus of this international conference, see for instance [2, 3].

The purpose of this presentation is twofold.

1. We give an overview of our work, [4, 5, 6], on reliable FEM and NSFD schemes in three settings of differential equations with different types of singularities, which are relevant in Mathematical Biology. The first setting is that of a one-dimensional singularly perturbed boundary value problem. We design a Singular Function Method (SFM) and a Mesh Refinement Method (MRF), which are proved to be theoretically and computationally uniformly convergent with respect to the perturbation parameter. The one-dimensional Burgers equation constitutes the second setting. We construct a NSFD scheme that preserves the boundedness and monotone decreasing properties of the kinetic energy. Finally, in the setting of a linear reaction-diffusion equation on a nonsmooth domain, we establish a bridge between the two reliable approaches by coupling NSFD discretizations in the time variable with the SFM or MRM in the space variables.

2. Whenever the data functions of the differential equations are smoother, we establish and restore optimal higher rates of convergence of the schemes despite the presence of singularities.

Identifying parameter values for oscillations in reaction networks

2023-04-21T16:04:54+03:00

In this work we present a method for identifying Hopf bifurcation points in parametric ordinary differential equations (ODE) models of reaction networks with n species. The method is based on a Hopf bifurcation theorem for parametric systems, algebraic geometry, majorization theory and convex analysis. The main difficulty related to identifying Hopf bifurcation points, lies with selecting parameter values such that the next to last Hurwitz determinant det H_{n-1} is zero. We show that a vertex of the Newton polytope of det H_{n-1} exists among the exponents of the product of diagonal entries of H_{n-1} which significantly reduces the computational effort. If such a vertex is associated with a negative monomial, then finding candidates for Hopf bifurcation points becomes an easy enough problem. We apply our method to several examples of biochemical networks such as a glycolytic reaction, Ca^{++} ions reaction and a simplified MAPK network.

An obesity and COVID-19 co-infection model

2023-04-14T15:47:13+03:00

Despite its rapid growth and having now reached endemic levels, obesity continues to grow at an alarming rate globally. Obesity is known to be an epidemic currently and we wish to model the evolution of obesity prior to, and now especially during the current COVID-19 times. The advent of COVID-19 resulted in increased deaths for the obese globally. We asses a dual-infection SEIR model with hospitalization and no cross-immunity. The results presented are key to understanding how the emergence of COVID-19 impacted already existing epidemics. The potential of such findings in quantifying the impact of future pandemics on existing epidemics is immense.

Mathematical modelling of the relationship between high blood pressure and diabetes: a multifactorial aprroach

2023-05-30T16:17:28+03:00

The increasing prevalence of high blood pressure (hypertension) and diabetes mellitus is a significant public health concern worldwide. These two chronic conditions often coexist and have been shown to amplify each other's adverse effects, leading to increased morbidity and mortality rates. Understanding the complex relationship between hypertension and diabetes is crucial for developing effective interventions and management strategies.

We propose a multifactorial mathematical model that integrates physiological, lifestyle, and environmental factors associated with hypertension and diabetes. The model is represented as a set of coupled ordinary differential equations (ODEs) decribe the change in the prevalence of hypertension, diabetes, and individuals with both conditions over time. Additionaly, we discuss potential applications of the model, limitations, and future direction for research in this area. Key components such as blood glucose and insulin dynamics, the renin-angiotensin-aldosterone system, and endothelial dysfunction, along with modifiable risk factors like diet, physical activity, and stress,are incorporated in the model. Additionally, the model considers the role of genetic predisposition and demographic factors in the development of these conditions.

A qualitative analysis of dog-mediated human rabies dynamics in Malawi: the role of multiple interventions in disease control

2022-11-29T13:12:20+02:00

Improved rabies surveillance or diagnostic systems can help curb rabies globally. In spite of studies suggesting that secondary interventions such as homeopathic or pre-or post-exposure prophylaxis (PEP) remedies can help reduce chances of infection after exposure; their unavailability, shortage in supply, and high cost of access mean that mass dog vaccination remains a key intervention for sub-Saharan Africa (SSA). However, characterizing the efficacy of mass dog vaccination, together with secondary interventions, may provide relevant information for understanding the disease dynamics and the development of policy measures in SSA. Premised on the notion that reliance on mass dog vaccination alone is insufficient to curb or control the spread of rabies, the current study proposes and presents a double compartmental model for evaluating the efficacy of multiple interventions in controlling the spread of rabies in Malawi. Qualitatively, the formulated model is analysed to assess the existence, positivity, and boundedness of the model solutions. To obtain the disease reproduction number(s), $R_0$, both at disease-free equilibrium (extinct) and endemic equilibrium (persistent) states for assessing the existence or persistence of dog-mediated human rabies in Malawi, we use the method of Next-Generation matrix. Using the model fitted data parameters, the half-normalization technique is employed to isolate key influential parameters for assessing rabies disease persistence or extinction. Since the proposed model provides room for investigating roles of other rarely modelled interventions such control of dog birth rate and use of PEP, the current study unravels key parameters influencing the dynamics of rabies disease in Malawi, thereby providing indicator measures for optimal control of the disease to the policyholders.

State constraints optimal control problems applied to ebola epidemic model

2023-04-14T15:24:41+03:00

Optimal control is a powerful tool that provide useful information in order to combat the progression of a disease by testing and comparing different vaccination strategies. In this talk, I will emphasize on vaccination of susceptibles individuals as control function, as well as on the number of available vaccines as state contraints to a Ebola model. In this direction, state constraints on the number of available vaccines can be studied after considering an appropriate cost functional to 8-dimensional nonlinear differential equations modeling the dynamics transmission of Ebola disease. Further, we analyze an optimal control problem where there is limitation on the supply of vaccines either in a fixed period of time or at each instant of time. The optimal control problem is solved analytically by maximum principle of Pontryagin type. Finally, a number of numerical simulations is performed in order to validate the analytical result.

Acknowledgements F.N. is supported by the Bulgarian Ministry of Education and Science, Scientific Programme "Enhancing the Research Capacity in Mathematical Sciences (PIKOM)", No. DO1-67/05.05.2022.

Analytical and numerical study of a diffusive predator-prey model incorporating an Allee effect

2023-05-01T15:52:29+03:00

In this study, we propose a diffusive predator-prey model incorporating an Allee effect for both: the predator and the prey. In more detail, the studied system of two non-linear partial differential equations represents variations of the population densities of the predator and the prey in the space and in the time due to a slow random diffusion process and local growth rates induced by an Allee effect and predator-prey interactions. An exact traveling wave solution of the proposed system is found applying the Simple Equations Method (SEsM). We simulate numerically the obtained analytical solution and show how the predator and the prey density waves can vary in its profile depending on the strength of the Allee effect.

Age-structured models of epidemiological dynamics

2023-05-31T15:17:55+03:00

The mathematical modeling of populations assumes that individuals initially move between different stages, where all individuals have the same probability of becoming infected (homogeneous populations) independent of aspects such as spatial location, the behavior of the people, and their ages. The last aspect is precisely one of the important characteristics that describe the heterogeneity in populations and infectious diseases. Individuals of different ages may have distinct reproductive and survival capacities of the virus. Also, diseases may have different infection and mortality rates depending on the age groups to which an individual belongs [1].

In the study of population dynamics of epidemics, age distributions allow for the characterization of the heterogeneity of populations. This feature is a factor with significant influence on the epidemic temporal passing, outcomes of transmission, and spread of infectious diseases [2]. The behavior of populations and the frequencies of individual interactions can vary among age groups. The differences produce a high degree of diversity in transmission rates. Individuals of different ages may have several levels of immunity to infectious diseases affecting the specific mortality and recovery rates depending on the age group to which they belong [3].

Age-structured epidemiological models are presented and analyzed from two mathematical approaches. The first is considering age in a discrete form based on systems of ordinary differential equations (ODE). Here the age of the different groups is considered like nodes, and their connections are given by transmission and aging. The stability of age subgroups is studied, and the reproductive number is calculated with vaccination R_v within a subgroup. The second approach considers the age structure from a continuous approach using partial differential equation (PDE) systems. In this model, the independence of time and age is assumed. Also, the existence, uniqueness, and stability of the endemic equilibrium when R_v > 1 is established and the best scenario to mitigate epidemic outbreaks is determined.

A general model of immune status

2023-03-20T15:30:14+02:00

The immune status is the concentration of specific antibodies, which appear after infection with a pathogen and remain in serum, providing protection against future attacks of that same pathogen. Over time the number of antibodies decreases until the next infection. During an infection, the immunity is boosted and then the immunity is gradually waning, etc. The densities of antibody concentration satisfy some partial differential equation with an integral boundary condition, which generates a stochastic semigroup. We present general results concerning asymptotic stability and sweeping of stochastic semigroups [1] and then we apply them to our model [2]. We also analyze special cases of the model, e.g. when immunity decreases exponentially; with constant increase of antibodies after infection; with a threshold concentration of antibodies at the re-infection; and with seasonal infections.

Mathematical modelling for CTCE-9908 (a CXCR4 inhibitor) on B16 F10 melanoma cell proliferation (Part II)

2023-03-24T16:42:21+02:00

The cell viability of tumour cells under treatment is an important quantitative measure of efficacy of that treatment. It is defined as the size of a treated population of cells expressed as a percentage of the size of a naturally growing population of the same cells. Hence, determining cell viability as a function of time is a crucial stage in the development of new cancer drugs. This function is frequently developed by interpolating the existing data using statistical techniques like regression. We use mechanistic modelling techniques rather than statistical tools to ensure that information on the dynamics of activation and inhibition is also included in the cell-viability function. We therefore derive a cell viability function in this presentation that is appropriate for experimental data collected from the inhibitory drug, CTCE-9980. Then, we use the experimental data to approximate the parameters at a 95% confidence interval. To validate the model, we use the bootstrapping technique to determine the stability of the estimated parameters at a 95% bootstrap confidence level.

The accuracy of predictions produced via interpolation, linear or nonlinear regression at any given value of an independent variable depends on the density of data points around this value. Predictions outside the domain adequately covered by data points can seldom be relied upon. Such predictions, often referred to as extrapolation, significantly depend on the type of functions used in the fitting process and, to a lesser extent, on the accuracy of the approximations of the data. To avoid the stated problem, the protocol followed here is focused on appropriately deriving a type of function to be used in the approximation/fitting process. More precisely, it consists of the following steps:
(i) A mathematical model of the processes tested in the experiment is constructed based on known quantitative relationships
(ii) The measured or observed variable is derived from the model in terms of its parameters.
(iii) The form of the theoretically derived observable determines the type of function to be fitted to the data. This is a function of the independent variable, which depends on a certain number of parameters.
(iv) The function in (iii) is fitted to the data to identify the values of the parameters.

This protocol follows the ideas in [1] and was applied in [2] to modelling and quantifying the inhibition of melanoma by L-Kynurenine. The specific advantage highlighted in this presentation is that the domain of validity of the approximation is determined by the domain of validity of the model and not the location of the data. Furthermore, we present the IC_50 as a function of time. The practical value of the latter is that one can obtain cell viability at a specific concentration and at a given time.

On an integrable version of the generalized totally asymmetric simple exclusion process on open chains

2023-05-01T15:57:33+03:00

We present here results from our study of a modified version of the generalized Totally Asymmetric Simple Exclusion process (gTASEP) on open tracks, which allows for analytic solution. We first note, that kinetics of protein synthesis is a process, which was first modeled by a variant of TASEP. Traffic-like collective motion on a single tracks are found in many non-equilibrium systems including many biological systems. Biological transport in cells and various other non-equilibrium systems are modeled by versions of TASEP.

In the gTASEP an extra interaction between the particles is included, besides the existing in the standard TASEP hard-core exclusion interaction. The additional interaction is modelled by the introduction of a second hopping probability p_m for particles, belonging to a cluster. The standard hopping probability p in the gTASEP applies only for single particles and the head (rightmost) particle of a cluster.

We explain concisely how one can arrive at the analytically solvable version of gTASEP through appropriate modification of the left (injection) boundary condition. We also give a short report of the main differences between the properties of the modified and the previously studied version of gTASEP on open tracks.

On the derivation of discrete time mathematics models for mutualist populations

2023-05-30T13:34:44+03:00

In this talk, we review different methods to derive discrete time model from continuous models. We apply the methods to continuous-time models of mutualism, and investigate the dynamics of the discrete models. For each discrete time model, we study parameter values for a coexistence equilibrium exists, then we investigate the asymptotic stability of the coexistence equilibrium and the emergence of a Neimark-Sacker bifurcation. Our results show that the outcome of the discrete time models depend strongly on their derivation from the continuous model. In particular the discrete model is not necessarily dynamically consistent with their continuous counterparts.

Time-scale separation in models for dengue fever

2023-04-10T15:50:04+03:00

Dengue fever is a vector-borne disease posing threat to millions of people. Its epidemiology is characterised by co-circulating multiple variants of the pathogen, the dengue virus. Mathematical modelling of dengue faces the challenges of finding a balance between accurate description of the disease dynamics, the different scales of modelling, and the associated levels of complexity which allow for establishing tractable causal relationships. One approach in modelling dengue and other vector-borne diseases has been to use host-only models that include the vector dynamics in an implicit fashion. However, these models are not directly suited for studies of intervention measures such as vector control or personal protection, which may influence the mosquito dynamics in a nonlinear manner.

We present the theoretical rationale that allows us to reduce the model complexity via a time-scale separation argument and rigorously derive the quasi-steady state approximation in models for vector-borne diseases using singular perturbation theory. This approach rests upon the observation that the dynamics of some phase variables can be taken as if in a quasi-steady state, and transforms the original system of ordinary differential equations into a system of algebraic-differential equations.

Then we discuss some issues which emerge repeatedly in the mathematical models of dengue: differences in structure (host-only vs. host-vector models), ecological effects due to seasonal changes in the vector population, immunological effects such as disease severity, and exert an effect on the dynamic behaviour of the model. Numerical bifurcation analysis is used to compare the bifurcation structure of a host-vector model of dengue (with two variants and reinfection) and its variant with reduced complexity resulting from a quasi-steady-state approximation to that of a previous host-only model of dengue. It turns out that in biologically-relevant parameter regimes, models with higher complexity (host-vector models) may exhibit fewer types of bifurcations and tend to have smooth dynamics (convergence to equlibria or limit cycles) compared to host-only models unless there is seasonal variation in the mosquito vector population.

Some aspects of mathematical modelling of cell cycle

2023-03-20T15:23:14+02:00

Modelling of cell cycle is one of the fundamental subject of mathematical biology because it could help to solve such problems as synchronization of cell division in cancer therapy and allows to understand dynamics of growth of cellular populations (e.g. tissues). There are many different models of cell cycles. In this talk we consider an age-size structured cell population model based on the cell cycle length [1]. The model is described by a first order partial differential equation with initial-boundary conditions. Using the theory of semigroups of positive operators we establish new criteria for an asynchronous exponential growth of solutions to such equations. We discuss the question of exponential size growth of cells. We study in detail a constant size growth model and a model with target size division. We also present versions of the model when the population is heterogeneous. The discussion on model generalizations will be a good excuse to present some new challenges in the study of asymptotic behaviour of semigroups of operators.

The impact of molecular docking programs and virtual screening in modern drug design

2023-04-13T16:17:36+03:00

Modern drug design heavily relies on computer-based methods. With the aid of computational methods, it is possible to predict the properties of compounds quickly and accurately, by calculating a large number of constants and coefficients. It is possible to predict the physical, chemical, and biological properties of compounds using computer methods, as well as their potential interactions with various receptors and enzymes.

The wide range of implemented software products enables users to choose one that allows them to extract the necessary information according to the problem to be solved and the most suitable for the specific technical and professional skills of the scientist [1, 2]. An overview of the most commonly used molecular docking and virtual screening programs, as well as the opportunities they offer for drug development, is presented in this work.

Demographic and epidemiological characteristics of animal bites in the North West Health Region, Algeria

2023-05-02T16:14:31+03:00

Animal bites, classified as a major zoonosis by public authorities in Algeria, are a common problem with 120 000 human bites occurring each year and between 15 and 20 cases of clinical human rabies.

In all, 116 403 animal bites were recorded in 2017 in Algeria, including 20 deaths. Of these, 73% occurred in Tell, 22% in Highlands and 5% in Sahara. The lowest incidence rate (30 bites per 100 000 people) was recorded in Adrar, a southern province, and the highest incidence (648 bites per 100 000 people) was recorded in Mostaghanem, a Northwest coast province. Half of the country's provinces had an incidence higher than the estimated national incidence of 279 human bites per 10 0000 inhabitants. Almost two-thirds of animal bites were caused by dogs and cat bites accounted for 30.5%.

The demographic and epidemiological characteristics, and spatial distribution of animal bites in the North West Health Region (NWHR) were profiled. Out of the 21 314 animal bites occurred in the NWHR during 2019, 71.3% were males. Of the 8275 bites occurred in children under 15 years, 66.8% were boys and 29.3% were children under 5 years. There was slight difference in animal bites occurrence between seasons and 58.7% of animal bites occurred outside dwellings. Most of the bites were of Category II (45.7%) followed by Category III (38.6%).

Dog bites are a significant source of morbidity and mortality and risk factors include young children and men. Educational, preventive, and informative programs are needed in addition to development of sustainable strategies against stray dogs.

Fat-tail test of regulatory DNA sequence

2023-04-26T16:43:47+03:00

Content-based computational methods for distinguishing between cis-regulatory element (CRE) and non-CRE are valuable for predicting CRE that have not been observed experimentally. The fluffy-tail test is one of the content-based CRE prediction methods. This is a bootstrapping procedure to identify abundant similar words with statistical significance in regulatory DNA, and then differentiate the regulatory DNA from non-CRE. The fluffy-tail test focuses only on the most frequently occurring subsequences in CREs, thus providing only a measure of homotypic transcription factor binding site (TFBS) clusters; however, most transcriptional regulatory regions contain multiple types of binding motifs; therefore, the fluffy-tail test may fail to capture statistical features arising from heterogeneous TFBS clusters in regulatory regions. In this paper, a kurtosis-based fat-tail test is proposed to measure both homogeneous and heterogeneous clustering. The results show that the fat-tail test separates CRE from non-CRE better than the fluffy-tail test.

Analysis of the transmission dynamics of pneumonia disease in a developing country: the effect of environment on pneumonia transmission, significance of hospital and community based care

2023-03-15T16:18:39+02:00

Pneumonia is recorded to be one of the major disease leading to serious deaths among the children aged under five and adults aged over 65. It is reported that, more than 2 million deaths occur in the developing countries due to pneumonia each year. The efforts for early detection, effective treatment and minimise the transmission of pneumonia are possible if the dynamics of the disease is well understood. In this research, a model for the transmission dynamics of pneumonia disease in a developing country to investigate the effect of environmental transmission, the significance of community and hospital based care is formulated. Basic properties of the model were computed. The basic reproduction number, R_0 was derived. The model has the disease-free and endemic equilibria. Sensitivity analysis was performed to determine the parameters with greatest significance in the reproduction number, from which the results revealed that transmission rate through environment and contact rate through person-to-person have the greatest potential of increasing the disease burden when increased. On the other hand, rate of treatment and decay rate of virus from the environment have greatest potential of minimising the number of new infections when increased. We computed the numerical simulations to illustrate the analytical results as well as establishing the long term behaviour of the disease. It was observed that treatment interventions either in the hospital or community can eradicate pneumonia infection. However, the infection may stay long in the community which might be as a result of increased contacts through unlimited visitors and crowded homes since they are not really controlled as compared to the hospital based care. Moreover, transmission of pneumonia is not only by person to person contact, but it can be transmitted through the environment. We therefore recommend trainings of more health workers to assist in the community on treatment and educating the individuals on transmission behaviour of pneumonia as well as ways to minimise spreading the infection. Moreover practising good hygiene, applying more control measures such as vaccination, disinfection and isolation is important to reduce the number of new infection to less than one.

Hybrid systems modeling of ecological population dynamics

2023-04-19T15:47:37+03:00

Discrete-time models are traditional for capturing the population dynamics of antagonistic interactions between two insect species - a host and its parasitoid [1].

These models are characterized by an update function that connects the population densities from one year to the next. While previously these update functions were chosen phenomenologically, here we introduce a hybrid approach for obtaining the update functions by solving ordinary differential equations that mechanistically capture the ecological interactions between the host and the parasitoid [2].

This hybrid approach is used to study the suppression of host density by a parasitoid. Our analysis shows that when the parasitoid attacks the host at a constant rate, then the host density cannot be suppressed beyond a certain point without making the population dynamics unstable. In contrast, when the parasitoid's attack rate increases with increasing host density, then the host population density can be suppressed to arbitrarily low levels [3].

These results have important implications for biological control where a natural enemy, such as a parasitoid wasp, is introduced to eliminate a pest that is the host species for the parasitoid. Finally, we further generalize these hybrid models to consider multi-species interactions, where multiple parasitoids attack a common host, or a single parasitoid attacks multiple host species [4].

Assessment of human proteins for potential tumour immunogenicity by in silico models

2023-05-30T13:31:48+03:00

Cancer is a major cause of death globally and has a major impact on societies across the world. Currently, existing cancer treatments possess several disadvantages, mainly associated with a lack of distinction between healthy and cancerous tissues. Thus, a more specific treatment approach is required. Cancer vaccines are a form of targeted immunotherapy that aims to prevent the occurrence or threat of existing cancer by educating the immune system about what cancer cells look like.

Immunogenic tumour proteins are predominantly mutated self-proteins recognized by the immune system and thus elicit strong, specific antitumor immune responses. However, spontaneous immune recognition of these mutations is inefficient. Because of that, immunogenic tumour proteins are promising candidates as personalized vaccines in the treatment of cancer. Ten years ago, a server for immunogenicity prediction of proteins of tumour origin, named VaxiJen, was developed in our lab. The models for immunogenicity prediction were derived by partial least square (PLS) discriminant analysis on sets of known immunogenic and non-immunogenic proteins. The primary structures of proteins were encoded by z-descriptors and transformed into uniform vectors by auto- and cross-covariance (ACC) calculations.

Our study aimed to collect a comprehensive dataset of human tumour antigens, which is to be used for deriving in silico models for the assessment of the immunogenicity of tumour proteins.

We manually searched the literature for human tumour antigens and looked for their protein sequences in the UniProt protein database. As a result, a set of 5199 antigens and 546 protein sequences was collected. We also collected a mirror set of 547 non-immunogenic tumour proteins using BLAST search of proteins of the human proteome against the collected dataset with tumour antigens and a subsequent check with the VaxiJen 2.0 web server for their tumour immunogenicity. The sets of immunogenic and non-immunogenic proteins were combined and randomly split into training and test sets in a ratio of 4:1.

The properties of each amino acid in the protein's primary structure were described by E-descriptors and the protein sequences were transformed into arrays with different lengths. An auto-cross covariance transformation of the protein arrays into uniform numerical vectors was applied to form a data matrix ready for modelling. We applied different machine learning algorithms using the Weka software on the data matrix of the training set and validated the derived models with the test set. The performance of the derived models was further evaluated.

The study found that the Quadratic Discriminant analysis, Random Forest, and Radial Basis Function classifier algorithms show the best predictive performance. The selected models will be implemented in a new version of the VaxiJen web server for the assessment of tumour immunogenicity of proteins and the discovery of potential candidates for cancer vaccines. This is an important step towards the development of effective cancer vaccines and personalized cancer treatment.

On the qualitative analysis of fractional-order impulsive gene regulatory networks

2023-03-16T16:29:10+02:00

A class of fractional-order impulsive gene regulatory networks (GRNs) is intestigated. The proposed model is an extension of some existing integer-order GRNs using fractional derivatives of Caputo type. Some qualitative properties of solutions such as stability and almost periodicity are studied and new criteria are established by the Lyapunov functions approach. The effects of time-varying delays and impulsive perturbations at fixed times on the almost periodicity are considered. Numerical example are also presented to justify our findings.

A mathematical model for compression of poroviscoelastic biological material like articular cartilage

2023-05-19T16:06:02+03:00

The articular cartilage consists of two main phases - solid phase and fluid phase. The solid phase is chiefly composed of complex macromolecules including collagen and proteoglycans. The fluid phase is presented by interstitial fluid filling in the solid phase’s pores and comprises up to 85 percent of the tissue by weight. The rheological behavior of such poroviscoelastic material during compression depends upon the intrinsic interaction between the solid matrix's deformation and the interstitial fluid's motion.

The mathematical model is based on the biphasic poroelastic (BPE) theory [1] which couples the interstitial fluid flow and matrix deformation. The model equations result in partial differential equations for the solid and fluid phases separately, which were solved numerically. For some practical applications, such as compression of cartilage, analytic solutions for the solid matrix deformation, fluid flow fields, and stress relaxation have been obtained. An optimization procedure, using experimental results [2], for estimation of the model parameters (hydraulic permeability and short-time and long-time relaxation) was elaborated.

Recently it has been shown [3] that the BPE model failed in predicting stress relaxation, that is, the flow-dependent viscoelastic mechanism is not able solely (coincidence 41.4% of the theoretical and experimental data) to cover the stress relaxation mechanism. In the current presentation we discuss on a several ways for combination of the fluid flow-dependent and fluid flow-independent viscoelastic mechanisms in accounting for the true mechanical behavior of articular cartilage under compression.

Acknowledgments. This work was supported by the Bulgarian National Science Fund - grant KΠ-06-H57/18.

Estimation of the parameters of the mathematical model for articular cartilage compression

2023-07-06T14:35:11+03:00

The mathematical model is based on the biphasic poroviscoelastic theory which couples the inter-porous fluid flow and solid matrix deformation. The material properties of the articular cartilage are presented by the elastic modulus, hydraulic permeability, and short-time and long-time relaxation. The model equations result in partial differential equations for the solid and fluid phases separately, which were solved numerically. For some practical applications, such as the compression of cartilage, analytic solutions for solid matrix deformation, fluid flow fields, and stress relaxation have been obtained. An optimization procedure, using experimental results, for the estimation of the model parameters was elaborated. The results suggest that the flow-dependent viscoelastic mechanism cannot solely cover the stress relaxation mechanism (coincidence 41.4% of the theoretical and experimental data). On the other hand, Fung's viscoelastic model was very successful at predicting stress relaxation with a 5.7% difference between the theoretical and experimental data.

Influence of the co-dynamics Ebola-COVID-19 in the population

2023-03-17T16:29:53+02:00

In this project, we investigate the influence of the co-circulation of Ebola virus and SARS-CoV-2 virus, which causes the COVID-19 pathology. Although no cases of co-infection of the two diseases have yet been reported, the observation of recent Ebola outbreaks shows that they have been of moderate incidence compared to those that preceded them, suggesting a possible influence of COVID-19 control on Ebola dynamics. We therefore propose a coupled Ebola-COVID-19 mathematical model. The models restricted to the COVID-19 pandemic and the Ebola epidemic, as well as the coupled model, are rigorously analysed. In each case, we show that the disease disappears when the basic reproduction number is less than one and that it is locally endemic when it is greater than one. For the coupled model in particular, we show the existence of several boundary equilibria, which can also be locally asymptotically stable under certain conditions, and of an interior equilibrium that can co-exist with the disease-free equilibrium point. Numerically, the restricted Ebola model is calibrated per phases for the outbreak in Democratic Republic of Congo (DRC) that took place between 2018 and 2020: (i) The first phase is the one were only the Ebola virus was circulating; (ii) The second phase is the one in which both viruses (Ebola and SARS-CoV-2 virus) were circulating. This calibration shows a significant variation of some parameters, which would be due to the implementation of measures addressed against COVID-19. An analysis of the reported data and the obtained parameters is proposed. Within the framework of the coupled model, we explore the impact of the increase or decrease of certain parameters of the dynamics of one disease on the dynamics of the other.

Impact of self-protection measures to reduce antibiotic resistant gonorrhoea infection

2023-04-12T16:17:57+03:00

A deterministic mathematical model for the transmission dynamics of gonorrhoea antibiotic resistance disease in a population is proposed and analysed. The model incorporates the classes of vaccinated individuals and individuals equipped with self protection measures to minimise antibiotic resistance cases. The threshold parameter R_0, the basic reproduction number, for the analysis of the model is calculated. In the given setting, the model exhibit a backward bifurcation for R_0<1.

For 100% vaccine of efficacy and recovery leads into permanent immunity, the model is without a backward bifurcation and the disease-free equilibrium is globally asymptotically stable whenever R_0<1. We show that the number of infectious individuals is smaller than that obtained in the absence of any intervention. Sensitivity analysis of the model is performed to determine the most influential parameters on the disease transmission dynamics. The optimal control analysis of the full model is presented. Numerical experiments are presented to support the theoretical analysis of the model.

Integrating mixed reality technologies in genomic data visualization and analysis for bioinformatics research

2023-05-01T15:49:45+03:00

With the advancement of Mixed Reality (MR) technologies and bioinformatics, researchers are exploring new ways to enhance the visualization and analysis of genomic data. The integration of MR technologies in bioinformatics research has the potential to revolutionize the way scientists interpret complex biological information. This article discusses the application of MR in genomic data visualization and analysis, highlighting its advantages in facilitating a more immersive and interactive experience. In particular, we will present case studies related to the implementation of the Unreal Engine in MR for bioinformatics research.

As part of the research, the role of intellectual property in bioinformatics will be analyzed, providing insights into its significance and implications in the field. The integration of MR can improve collaboration among researchers and assist in the understanding of intricate patterns within genomic datasets. Furthermore, the article examines the challenges faced in implementing MR technologies in bioinformatics and addresses possible solutions to overcome these obstacles.

Overall, the integration of Mixed Reality in bioinformatics research has the potential to reshape the field and drive innovation in genomic data analysis.

Modeling the COVID-19 incorporating variants and vaccines

2022-12-23T16:30:37+02:00

Since the new coronavirus SARS-CoV-2 was detected in China in 2019, many mathematical models have been developed to study the possible evolution of the COVID-19 disease [1,2]. By the end of 2020, with the supply of the different vaccines and the appearance of new more contagious variants, we presented a model that took into account these two determining facts, showing its performance with real data from Italy [3]. In this talk, we will summarize the proposed models. The modeling framework can incorporate new variants as they emerge to give critical insights into the new cases and guide public policy decision-making concerning vaccine roll-outs and reopening strategies.

Weakly reversible realizations of Biochemical Systems Theory (BST) models

2023-05-18T14:54:12+03:00

Biochemical Systems Theory (BST) is a modeling framework that uses power law formulations so that nature's nonlinearities and heterogeneity can be well taken into account. It has been recently found out that reaction networks can represent BST models. However, many results in Chemical Reaction Network Theory (CRNT) require that the reaction network be weakly reversible which is usually not the case for BST models. Hence, this paper aims to obtain an algorithm to construct a weakly reversible realization of two variants of BST models which are S-systems and General Mass Action (GMA) systems.

The algorithms are based on the notion that fixing the stoichiometric matrix of the initial network preserves the dynamics of the system. For S-systems, it was done via association of reactions for the influx and efflux terms of the model such that the same set of reaction vectors are generated with the initial reaction network representation. On the other hand, GMA systems made use of matrix factorization via solving a linear system. However, the algorithm becomes impractical for large GMA systems which is then remedied by considering poly-PL kinetics and applying the algorithm for S-systems.

This paper enables us to analyze BST models using results on CRNT such as on the non-emptiness of the system's set of positive steady states. Furthermore, it enriches the field of CRNT because the proposed methods here allow us to construct a weakly reversible reaction network with power law formulations.

Modelling horizontal gene transfer of plasmid-mediated resistance in biofilms

2023-05-01T16:15:28+03:00

The global spread of antibiotic microbial resistance (AMR) is an increasing health concern, and has been mainly attributed to antibiotics abuse and misuse [1]. Dissemination of AMR is largely associated to plasmids, extrachromosomal genetic elements able to transfer to new host cells through conjugation, which plays a crucial role in the ecological success of plasmids in bacterial communities. Even at subinhibitory concentrations, metals exert a selective pressure on bacterial communities, hence promoting dissemination of AMR. However, in the absence of selective pressure, this ecological success contrasts with the high costs of plasmid maintenance and very low rates of conjugation, generating the so called plasmid paradox [2].

Horizontal gene transfer is even more relevant in biofilms, where close physical contact between bacteria facilitates conjugation. This study presents a mathematical model simulating the social behaviour of bacteria regulating plasmid transfer under selective pressure from metals and more specifically in the case of co-resistance and cross-resistance to antibiotics and metals within a growing biofilm. The model is formulated as a nonlocal system of hybrid PDEs with a convolution integral regulating the transfer genes expression. Gene expression is modelled as a rate depending on environmental conditions: toxic stress from metals and antibiotics, and the presence of potential receptors around a donor, called recipient-sensing. Based on experimental results from literature, a promotion function is also introduced to account for the increase in conjugation in the presence of trace metals.

This mathematical ecology study aims to give an insight into how bacterial social behaviour might answer the plasmid paradox, and how metal contamination participates in the spread of AMR. Numerical simulations showed that the model is able to qualitatively reproduce the influence of conjugation on plasmid dynamics in a growing biofilm. The relative influence of conjugation and vertical gene transfer was compared, including under selective pressure exerted by trace metals.

Pursuit-evasion dynamics in predator-prey models

2023-05-17T16:22:36+03:00

We study a pursuit-evasion predator-prey model (equation 1, see PDF), where P and N denote predator and prey densities while W is the chemical density. The reaction functions f and g describe local predator-prey interactions and birth/death processes, d_P, d_N, d_W > 0 are diffusion constants, ξ, η > 0 are taxis sensitivity parameters, γ and μ are rate coefficients related to the production and degradation of the chemical secreted by the predators. The taxis term in the first equation describes direct prey taxis, i.e. the movement of predators towards the density gradient of prey (pursuit) while the second equation represents situation in which the prey senses not the presence of predators themselves but rather their odor, a diffusive chemical with density W secreted by the predators so that the prey use evasive strategy moving in the opposite direction with respect to the gradient of W. System (1) is supplemented by initial conditions and no-flux boundary conditions describing the lack of migration through the boundary of a region where the species under consideration are distributed.

We shall present results published in [1, 2] and some yet unpublished on the existence of global-in-time solutions and formation of space-time patterns for the range of parameters when a space-homogeneous coexistence steady state looses it's stability. On assuming the reaction part of the model of the classical Bazykin type we find some biologically relevant modifications in the taxis part of the model such that the blow-up of solution in finite time is prevented for a broad class of initial data.

The results are illustrated by various numerical simulations.

Nonhomogeneous multitype Markov branching stochastic processes as models of cell population dynamics

2023-04-12T15:31:21+03:00

We consider multitype Markov branching processes with immigration occurring at time points generated by Poisson random measures. Limiting behavior of the processes for different rates of the Poisson random measures in subcritical, critical and supercritical cases is investigated and various limiting distributions are obtained. In particular, results analogous to a strong LLN (Law of Large Numbers) and a CLT (Central Limit Theorem) are proved. These models find applications to study evolution of multitype cell populations in which new cells join the population according to a time-varying immigration mechanism. For instance, terminally differentiated cells and their progenitors are replaced by diffrrentiating stem cells. As another example, a four-type model can be formulated to study evolution of genetic variation within a cell population at a specific base position of the genome by letting each of the 4 types represents one of the four nucleotides: A, G, C, and T.

On an optimal control problem arising from the tumor treatment

2022-11-28T17:02:58+02:00

In this talk we will discuss a mathematical model which describes the tumor growth in animals. The mathematical model is governed by a nonlinear reaction-diffusion system. We first use some PDE techniques to establish the global existence and uniqueness as well as the long-time behavior of the solution for the system. We then turn the attention on the optimal drug dosage for the tumor treatment. It is shown that under certain conditions there exists an optimal drug dosage for the problem. The result could be potentially used in the medical science in designing the automation of drug usage for some diseases.

Quantifying noise modulation from coupling of stochastic expression to cellular growth: an analytical approach

2023-04-19T15:55:38+03:00

The overexpression of many proteins can often have a detrimental impact on cellular growth. This expression-growth coupling leads to positive feedback - any increase of intracellular protein concentration reduces the growth rate of cell size expansion that in turn enhances the concentration via reduced dilution. We investigate how such feedback amplifies intrinsic stochasticity in gene expression to drive a skewed distribution of the protein concentration. Our results provide an exact solution to this distribution by analytically solving the Chapman-Kolmogorov equation, and we use it to quantify the enhancement of noise/skewness as a function of expression-growth coupling. This analysis has important implications for the expression of stress factors, where high levels provide protection from stress, but come at the cost of reduced cellular proliferation. Finally, we connect these analytical results to the case of an actively degraded gene product, where the degradation machinery is working close to saturation.

Novel acetylcholinesterase inhibitors developed by structure-based drug design in DDBL@MUS

2023-04-11T15:53:57+03:00

The inhibitors of the enzyme acetylcholinesterase (AChE) improve impaired cognitive functions due to increased levels of the neurotransmitter acetylcholin. They are widely used for symptomatic treatment of neurodegenerative diseases like Alzheimer's disease (AD). Among them, galantamine (GAL) is the most frequently prescribed drug.

Here, we describe the discovery and development of several GAL derivatives as multitarget agents against AD using structure-based methods for drug design. Initially, two libraries of derivatives were designed. The first library included hybrid molecules between GAL and novel AChE inhibitors that we previously discovered by in silico screening of compounds from ZINC database. The second library included hybrid molecules between GAL and curcumin (CU). The compounds were tested in silico for permeability across the intestinal mucosa and the blood-brain barrier (BBB), then docked into the binding site of human AChE. Among the best-scored compounds, one from the first library and 14 from the second library were selected, synthesized and tested in vitro for neurotoxicity and anticholinesterase activity. The compound from the first library was found to be non-toxic and 68 times more active than GAL. From the second library, 5 compounds were more active than GAL and less toxic than CU. The most active compound, named 4b, was 186 times more active than GAL. It was additionally tested for anticholinesterase, antioxidant and antiamyloid activity in vitro, in vivo and ex vivo. In all tests, the new GAL-CU hybrid 4b outperformed its parent compounds GAL and CU and emerged as a promising multitarget agent for the treatment of neurodegenerative diseases.

This project is funded by the Bulgarian National Science Fund (Grant DN03/ 9/2016), the Bulgarian National Roadmap for Research Infrastructure (Grant D01-271/2019) and the Science and Education for Smart Growth Operational Program cofinanced by the European Union through the European Structural and Investment funds (Grant BG05M2OP001-1.001-0003). All results obtained under the project have been published. The publications are freely accessible at: http://www.ddg-pharmfac.net/.

Mechanisms of cancer invasion and progression: insights from cellular automaton models

2023-04-18T13:42:18+03:00

Tumour invasion and progression may be viewed as collective phenomena emerging from the interplay of biological cells with their environment. Cell-based mathematical models in which cells are regarded as separate discrete entities can be used to decipher the rules of interaction. Here, we focus on the dynamics of glioma and breast cancer.

We introduce lattice-gas cellular automaton models [1, 2] to analyse the role of phenotypic plasticity in cancer invasion, define spatial and non-spatial Moran processes to shed light on the size of the tumour originating niche, and adopt Markov chain models to investigate the origin of genetic heterogeneity in glioblastoma [3, 4, 5].

Exploring the spatial tissue environment: non-local modelling, applications, numerical challenges

2023-04-11T15:08:24+03:00

A partial differential equation (PDE) model of the spatio-temporal evolution of cell populations which interact in a spatially nonlocal fashion with and between themselves has been introduced in the landmark paper [1] by Armstrong, Painter, and Sherratt in 2006. Since then, their basic approach has been incorporated in numerous biomedical models and, along this way, it has been refined, extended, analysed, and implemented. The range of applications, to name a few, includes adhesion-driven pattern formation of cellular populations, tumour invasion of host tissue, wound healing dynamics, and neural crest cell dispersal in developmental biology.

In this presentation, we start from the basic model [1] and its mathematical properties, like mass conservation and non-negativity, and extend it to include volume filling terms as well as attracting and repelling interactions. A Turing-like analysis then sheds light on parameter ranges which allow for pattern formation starting from spatially perturbed homogeneous steady states. The consideration of cross-diffusion within such models is presented and gives rise to a further qualitative improvement of the model. The nonlocal nature of the model also necessitates a look at the formulation of suitable boundary conditions.

Spatially nonlocal terms in a PDE model constitute a computational challenge for model simulation, in particular for spatial dimensions higher than one. This challenge arises because the matrices representing the approximation of nonlocal terms are not sparse and thus, in general, computationally expensive. Here we present a finite volume framework which makes use of Fast Fourier Transform techniques to allow for an efficient treatment of these terms under some suitable side conditions. We also touch upon the issue of non-negativity preservation which is ensured by the scheme presented.

Controlled branching processes as models for logistic population growth

2023-04-18T14:24:07+03:00

Controlled branching processes (CBPs) are stochastic growth population models in which the number of individuals with reproductive capacity in each generation is determined by random control functions. This kind of processes is flexible enough to model the evolution of different kind of populations including populations with logistic growth. The logistic population growth is characterized by an initial approximately exponential growth of the number of individuals till they reach an equilibrium value around which they fluctuate. This equilibrium value mainly depends on the carrying capacity of the population.

In this work, we first deal with the modeling of populations with logistic growth through CBPs. Classical deterministic models (such as Verhulst model, θ-logistic model -including Ricker model-, Hassell model -including Beverton-Holt model- or Gompertz model) will find stochastic counterparts based on suitable definitions of CBPs with binomial control functions. These binomial control laws will have a success probability depending on the current population size, carrying capacity and offspring mean.

Secondly, to guarantee the applicability of the introduced processes to model real data sets, we develop the estimation theory of its main parameters. We tackle this problem in the general framework of the CBP, considering a Bayesian perspective. Our aim is to estimate the posterior distributions of the main parameters of the CBP using approximate Bayesian computation and sequential Monte Carlo methods. We illustrate the accuracy of the proposed methodology by analyzing real data sets corresponding to populations with logistic growth using the statistical software R.

The results presented in the talk are part of the recent paper [1].

Multitype controlled branching process as a model for progenitor cell populations

2023-04-18T14:31:48+03:00

We focus our attention on a specific biological application with the purpose of describing progenitor cell populations cultured in vitro. This problem was firstly treated in [1]. The population considered consists of two types of cells: the progenitor cells or type T<sub>1</sub> cells (immediate precursors of oligodendrocytes) and the oligodendrocyte cells or type T<sub>2</sub> cells (terminally differentiated oligodendrocytes). The development of these cells is as follows: oligodendrocytes rise from precursor cells; precursor cells can die without any offspring cell, can split off into two daughter cells of the same type or can terminally differentiate into oligodendrocytes, which do not have reproductive capacity. Moreover, there is a presence of censoring effects due to the migration of progenitor cells out of the microscopic field of observation. They modelled this biological system as a two-type age-dependent branching process with emigration, where the emigration models the effect of censoring. The authors developed the estimation of the offspring distribution in a frequentist context.

This work continues with the aforesaid line of research, tackling this problem from a different and richer perspective by considering the class of controlled branching processes, and by making use of the Bayesian outlook. The results that we present in this talk have been recently published in [2].

Mathematics of malaria transmission dynamics: the renewed quest for eradication

2023-04-10T16:12:51+03:00

Malaria - a deadly disease caused by protozoan Plasmodium parasites - is spread between humans via the bite of infected adult female Anopheles mosquitoes. Over 2.5 billion people live in geographies whose local epidemiology permits transmission of P. falciparum, responsible for most of the life-threatening forms of malaria. The widescale and heavy use of insecticide-based interventions, notably long-lasting insecticidal nets and indoor residual spraying), during the period 2000-2015, resulted in a dramatic reduction in malaria incidence and burden in endemic areas, prompting a renewed quest for malaria eradication. Numerous factors, such as Anopheles resistance to all currently-available insecticides and anthropogenic climate change, potentially pose important challenges to the eradication efforts. In this talk, I will discuss a genetic-epidemiology framework for assessing the impact of insecticide resistance on malaria. Specifically, questions on whether eradication can be achieved using existing insecticide-based control resources will be addressed. There may be a brief discussion on the utility of some of the gene drive-based biological interventions being proposed as a plausible alternative pathway for achieving the laudable malaria eradication goal.

A stochastic model to mathematically describe the dynamics of long-lived raptor species

2023-04-11T15:37:28+03:00

The main motivation behind this talk is the study of stochastic models to describe the demographic dynamics of long-lived raptor species. The methodology based on population viability analysis, considered in conservation biology and in the management of threatened or endangered species, usually requires information about several variables (sizes, ages, mortality rates, growth rates, environmental variables, etc). In practise, taking into account the particular characteristics of these raptor species (monogamous behaviour, stability of their couples, marked natal philopatry, similar reproductive strategy, etc) real data about such variables are difficult to obtain. Mathematical models based on others methodologies have not been sufficiently investigated. In this biological scenario, branching processes could provide appropriate mathematical models.

We present a model that requires an information feasible to be observe. It considers the calendar year as unity of time and assumes an environment changing, stochastically in time, influenced by the reproductive age of the females. From such a model, we investigate several inferential problems of ecological interest for these raptor species. In particular, with the purpose to forecast possible changes in their population dynamics, we estimate the most relevant reproductive parameters included in the mathematical model. To this purpose, we use a procedure based on Approximate Bayesian Computation methods.

This statistical methodology requires to perform a large number of simulation from the probability model. The parameters necessary to carry out these simulations are generated from a suitable prior distribution based on the previous knowledge of the species under study. As illustration, using real data of counts of the number of couples in the population, we apply the proposed methodology to describe the demographic evolution of two black vulture colonies located in the region of Extremadura (Spain) which are considered both the largest and densest breeding colonies worldwide.

Mathematical challenges in triggered drug delivery: getting the right dose to the right place at the right time

2023-04-12T13:15:18+03:00

The brain tissue is protected by the blood-brain barrier: a wall of tightly-packed cells that keep unwanted molecules from crossing from the blood vessels into the tissue. This presents challenges to delivering therapeutic drugs to locations in the brain to treat certain diseases. One approach to meeting this challenge is to encapsulate the drugs in sono-sensitive nano-carriers. These vesicles can then be made to release their cargo locally using focused ultra-sound beams at intensities that are not damaging to the surrounding tissue. Mathematical problems come up when trying to answer questions such as: How can we describe the kinetics of drug transport and distribution through the tissue? What is the best positioning for an array of ultrasound transducers in order to produce the required signal at the right spot in the brain? What ultrasound parameters and dosages produce the the desired drug profile at the target region?

In this talk I will discuss the specific mathematical challenges, as well as some approaches to their solution.

This is joint work with Peter Hinow (University of Wisconsin in Milwaukee).

Modeling biological systems using dynamical survival models. Lessons from the recent pandemic.

2022-11-29T14:47:17+02:00

In the talk I will briefly outline the basic idea of the so-called dynamical survival analysis (DSA) which is a framework for using survival analysis methods to build approximate models of individual level ecological dynamics based on mean-field approximations. I will show the DSA connection with the classical agent based models for epidemics as well as certain frailty models that have been successfully applied to analyzing the recent COVID-19 epidemic.

Modelling cellular processes: from single cells to collective behaviour

2023-04-10T16:02:07+03:00

Living organisms are multi-scale systems organized at multiple levels. In nature, organisms can exist both as single cells, or, in multi-cellular forms. Diversification of forms and functions have led to the explosion of the variety of living beings among the prokaryotes, eukaryotes, plants and animals in our world. In higher multicellular organisms, single cells organize into tissues, which then form organs made with one or more types of tissues. For example, in humans, spatiotemporal organization of different organs performing different vital functions make up a whole body. The body functions properly only when all these constituent levels work coherently in an inter-dependent manner. Each cell, which is the lowest constituent of any living organism, has a well-structured interior with different organelles and large and small molecules doing different biochemical and biophysical reactions. Single and multi-cellular functional dynamics are regulated by these multi-step feedback/feed-forward regulated intra- and inter-cellular biochemical reactions.

Here, I will use a minimalist theoretical approach, with model cells having a simple set of regulated biochemical reactions, to elaborate the dynamics exhibited in a single cell, and in a group of cells having diffusive interactions among them. Using mathematical models of the pathways, first the role of types of feedbacks (negative and positive, single and coupled) on the single cell dynamics will be shown. Many different types of simple and complex dynamics like mono- and multi-stable states, oscillatory, and chaotic dynamics can be observed in these model single cells, which have correspondence in natural systems. Presence of fractal basins are also observed, which may underlie the occurrence of phenotypic variations observed in the same system in different environments. In multi-cell systems, their collective behaviour is studied for different tissue size, regular and random inter-cellular interaction strengths, etc. How complex dynamics in individual cells get suppressed (control) or enhanced (anti-control) in coupled cells are also discussed. These studies are summarized to give a view of dynamical changes that interacting systems can show at different organizational scales.

Modeling phage-bacteria interactions and phage therapy as an alternative to bacterial multidrug resistance

2023-04-11T14:55:39+03:00

The World Health Organization has sounded the alarm on increasing appearance of bacterial resistance and multi-resistance to existing antibiotics which causes millions of human deaths per year. Faced with this therapeutic impasse, there is a renewed interest in the use of phages (or bacteriophages), which are harmless to humans, but bacteria-eating viruses, as a reliable alternative to combat this scourge, especially since the use of phages for therapeutic purposes or phage therapy is an ancient practice that dates back more than a century and has been successful and continues to be practiced in Eastern Europe.

During this plenary presentation, I will give a brief history of phage therapy since 1917, and emphasize a review of the literature on mathematical models of bacterium-phage interactions and phage therapy described by differential equations. I will conclude this with a detailed presentation of age-since-infection structured model, taking into account spontaneous prophage induction in the presence of lytic and temperate phages.