Mathematical analysis of a fish-plankton eco-epidemiological system

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Résumé

In this paper, we have formulated and analyzed a mathematical model describing the dynamics of the phytoplankton producing toxin and the fish population by using an ordinary differential
equations system. The phytoplankton population is divided into two groups, namely infected phytoplankton and susceptible phytoplankton. We aim to analyze the effect of the toxic substance on the
fish population. The equilibria stability of the model has been studied locally and globally around
the basic reproduction ratio R0. The mathematical analysis of the model shows that the equilibrium
without disease is globally asymptotically stable if R0 ≤ 1 and the endemic equilibrium is globally
asymptotically stable if R0 1. Numerical simulations are carried out to illustrate the feasibility of
the theoretical results

Mots-clés

susceptible phytoplankton, basic reproduction ratio, fish, global stability, viral, infection