Dynamical analysis of an eco-epidemiological model experiencing the crowding effect of infected prey

Abstract

Most eco-epidemiological models use a bi-linear functional response, also known as the simple law of mass action, to describe the transmission of an infection. The non-linear incidence rate considers the infected individuals' crowding effect and prevents the contact rate's unboundedness by choosing suitable parameters. This paper aims to construct an Eco-Epidemiological model following the nonlinear incidence rate suggested by Gumel and Moghadas 2003. The model also offers a reasonable, realistic approach to the ecological systems in the world as we follow the Holling type II for the predator-susceptible prey interaction and the simple mass action low for the predator for the predator-infected prey interaction as the infected prey would be weak. The time for finding it would be significantly more than the time needed to catch the healthy prey. We proved the solutions' positivity and existence and our model's boundedness. The equilibrium points are determined with the feasibility conditions for each. Local stability has been analysed using Routh Hurwitz, and a Lyapunov function has been constructed to study global stability according to La Salle theorem. Different types of bifurcation are observed using Sotomayor’s and Hopf theorems. The numerical analysis of the solution was carried out using fourth-order Runge-Kutta. The simulations that we performed using MATLAB 2022a supported our theoretical findings.