Abstract
In this article, the dynamical behavior of a three dimensional continuous time eco-epidemiological model is studied. A prey-predator model involving infectious disease in predator population is proposed and analyzed. This model deals with SI infectious disease that transmitted horizontally in predator population. It is assumed that the disease transmitted to susceptible population in two different ways: contact with infected individuals and an external sources. The existence, uniqueness and bounded-ness of the solution of this model are investigated. The local and global stability conditions of all possible equilibrium points are established. The local bifurcation analysis and a Hopf bifurcation around the positive equilibrium point are obtained. Finally, numerical simulations are given to illustrate our obtained analytical results.
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