Mathematical Models with Generic Birth and Death Rates in Population Dynamics
DOI:
https://doi.org/10.11145/cb.v3i1.650Abstract
Mathematical modelling is an important tool in population dynamics that allows describing various biotechnological and ecological processes.
The classical models (e.g., the Monod-type models, modelling microbial growth or the Rosenzweig-MacArthur predator-prey model, among others) assume a per capita growth rate that is linear w.r.t. the food intake and a constant per capita death rate.
In the present work, we consider generic birth and death rates based on several observations proposed by A.J. Terry.
For sufficiently small values of the consumption, the reproduction will be zero rather than linearly increasing. Also, there will always be a limit to the rate at which an individual can reproduce.
On the other hand, every organism needs some minimal energy intake, in order to survive. Therefore, under this threshold the death rate should be higher.
Using the idea of non-linear birth and death rates, we propose models that are generalizations of classical models in population dynamics. We study the asymptotic properties of the solutions of the considered models. We show that in some cases those models have much richer dynamics and, thus, allow us to model more complex behaviour of the biological system. Also, we investigate their ability to model real processes by comparing the results of the parametric identification process to experimental data for different microbial cultures.
Downloads
Published
Issue
Section
License
The journal Biomath Communications is an open access journal. All published articles are immeditely available online and the respective DOI link activated. All articles can be access for free and no reader registration of any sort is required. No fees are charged to authors for article submission or processing. Online publications are funded through volunteer work, donations and grants.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
