Dynamics of an Eco-Epidemiological Model with Saturated Incidence Rate

In this paper we study the effect of prey infection on the modified Leslie-Gower predator-prey model with saturated incidence rate. The model will be analyzed dynamically to find the equilibria and their existence conditions as well as their local stability conditions. It is found that there are six type of equilibria, namely the extinction of both prey and predator point, the extinction of infective prey and predator point, the extinction of predator point, the extinction of prey point, the extinction of infective prey point and the interior point. The first four equilibrium points are always unstable, while the last two equilibria are conditionally stable. We also find that the system undergoes Hopf bifurcation around the interior point which is controlled by the rate of infection. To illustrate our analytical results, we show some numerical results.