A diffusive predator-prey mathematical model with disease in prey population

Abstract

A three dimensional mathematical model of predator-prey system with disease in prey population is proposed. The reaction-diffusion equations are used to study stability under diffusion. In this model, it is assumed that the disease transmission occurred according to mass action law. Thus prey population is divided into two groups: one being the susceptible prey and another being the infected prey. Aim of this study is to provide the dynamics of the system without diffusion and with diffusion. Global stability of the system about the positive interior equilibrium point with the help of LaSalle’s principle is to be studied. Coexistence of all the species with homogeneous biomass distribution is shown in the study. The analytical findings are supported by numerical observations.