Abstract
We proposed and analyzed a predator–prey model. The disease effects in predator due to pollution in environment, as well the immigration factor effected is discussed. We assumed that, the population are divided into three parts prey, susceptible predator and infected predator. Firstly, the existence, uniqueness and bounded-ness of the solution of the model are discussed. Secondly, we studied the existence and local stability of all equilibrium points. Furthermore, some of the Sufficient conditions of the global stability of the positive equilibrium are established using suitable Lyapunov functions. Finally, those theoretical results are demonstrated with numerical simulations.
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