Mathematical analysis of a fish-plankton eco-epidemiological system

Abstract

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 equation 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.