Modélisation Mathématique des Populations en Interactions

Abstract

The purpose of this thesis is the mathematical study of the dynamics of interacting populations. We use ordinary differential equations as the main modeling tool to analyze the local and global stability of fundamental models of Lotka-Volterra (predator prey), competition and mutualism, then a system of three populations (rabbits, sheep, wolves).

Then we extend this study to more complex systems integrating the epidemiological di- mension.