Math. Model. Nat. Phenom.
Volume 16, 2021
Mathematical Models and Methods in Epidemiology
|Number of page(s)||32|
|Published online||28 June 2021|
Effects of heterogeneity and global dynamics of weakly connected subpopulations
Department of Mathematics, California State University,
2 Université de Lorraine, CNRS, Inria, IECL, 57000 Metz, France.
3 Department of Mathematics, University of Tlemcen, Tlemcen 13000, Algeria.
* Corresponding author: email@example.com
Accepted: 6 June 2021
We develop a method that completely characterizes the global dynamics of models with multiple subpopulations that are weakly interconnected. The method is applied on two classes of models with multiple subpopulations: an epidemic model that involves multiple host species and multiple vector species and a patchy vector-borne model. The method consists of two main steps: reducing the system using tools of large scale systems and studying the dynamics of an auxiliary system related the original system. The developed method determines the underlying dynamics and the “weight” of each subpopulations with respect to the dynamics of the whole population, and how the topology of the connectivity matrix alters the dynamics of the overall population. The method provides global stability results for all types of equilibria, namely trivial, boundary or interior equilibria.
Mathematics Subject Classification: 92D30 / 34D23 / 34D20 / 34D40 / 34A34
Key words: Large scale systems / network configuration / weakly connected populations / global stability / Lyapunov functions
© The authors. Published by EDP Sciences, 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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