Parameter sensitivity analysis for CO-mediated sickle cell de-polymerization

Liping Liu, Mufeed Basti, Yao Messan, Guoqing Tang, Nicholas Luke — Thu, 14 Mar 2024 00:00:00 +0200

This study investigates the impact of melting/binding rates (referred to hereafter as the parameters) over the polymers and monomers on the dynamics of carbon-monoxide-mediated sickle cell hemoglobin (HbS) de-polymerization. Two approaches, namely the traditional sensitivity analysis (TSA) and the multi-parameter sensitivity analysis (MPSA), have been developed and applied to the mathematical model system to quantify the sensitivities of polymers and monomers to the parameters. The Runge-Kutta method and the Monte-Carlo simulation are employed for the implementation of the sensitivity analyses. The TSA utilizes the traditional sensitivity functions (TSFs). The MPSA enumerates the overall effect of the model input parameters on the output by perturbing the model input parameters simultaneously within large ranges. All four concentrations (namely, de-oxy HbS monomers, CO-bound HbS monomers, de-oxy Hbs polymer and CO-bound HbS polymer) as model outputs, and all four binding/melting rates (namely, the CO binding and melting rates for polymers and monomers) as input parameters are considered in this study. The sensitivity results suggest that TSA and MPSA are essentially consistent.

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

Atanas Atanasov, Slavi Georgiev, Lubin Vulkov — Wed, 24 Apr 2024 00:00:00 +0300

Several models on honeybee population dynamics have been considered in the past decades, which explain 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 of 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 the 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 model equilibria stability 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.

BIOMATH

Parameter sensitivity analysis for CO-mediated sickle cell de-polymerization

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