Mathematical study of eco-epidemiological system

Abstract

In this paper, a mathematical model consisting of the prey- predator involving infectious disease in prey population, is proposed and analyzed. And this disease passed from a prey to predator through attacking of predator to prey. The model represented mathematically by the set of nonlinear differential equations. The existence, uniqueness and boundedness of the solution of this model are investigated. The local and global stability conditions of all possible equilibrium points are established. The occurrence of local bifurcation (such as saddle-node, transcritical and pitchfork) a long with Hopf bifurcation near each of the equilibrium points are discussed. Finally, numerical simulation is used to study the global dynamics of this model.

Keywords: eco-epidemiological model, SI epidemics disease, prey-predator model, stability analysis, Hopf bifurcation.