Study of LG-Holling type III predator–prey model with disease in predator

In this article, a Leslie–Gower Holling type III predator–prey model with disease in predator has been developed from both biological and mathematical point of view. The total population is divided into three classes, namely, prey, susceptible predator and infected predator. The local stability, global stability together with sufficient conditions for persistence of the ecosystem near biologically feasible equilibria have been thoroughly investigated. Boundedness and existence of the system are established. All the important analytical findings have been numerically verified by using program software MATLAB and Maple.