The dynamicics of a prey- predator model with the existence of disease and pollution

Abstract

An eco-epidemiological model consisting of a prey-predator system involving disease and pollution has been proposed and studied. It is assumed that the disease transmitted between the individual of prey species by contact with nonlinear incidence rate, however the predator preys upon  the prey according to Holling type-II functional response. The existence, uniqueness and boundedness of the solution of the system are studied. The existence of all possible equilibrium points are discussed. The local stability of for each equilibrium point is investigated. The global stability of the positive equilibrium point is studied with the help of Lyapunov function. Finally further investigations for the global dynamics of the proposed system are carried out with the help of numerical simulations. It is observed that the system has a Hopf bifurcation near the positive equilibrium.