A Complex Dynamic of an Eco-Epidemiological Mathematical Model with Migration

Abstract

In this paper, we propose an eco-epidemiological mathematical model in order to describe the effect of migration on the dynamics of a prey–predator population. The functional response of the predator is governed by the Holling type II function. First, from the perspective of mathematical results, we develop results concerning the existence, uniqueness, positivity, boundedness, and dissipativity of solutions. Besides, many thresholds have been computed and used to investigate the local and global stability results by using the Routh–Hurwitz criterion and Lyapunov principle, respectively. We have also established the appearance of limit cycles resulting from the Hopf bifurcation. Numerical simulations are performed to explore the effect of migration on the dynamic of prey and predator populations.