The dynamics of prey-predator model with harvesting involving diseases in both populations

In this paper, a mathematical model consisting of the prey-predator model with different infectious diseases that spreads in both population and harvesting in the infected population. It is assumed that the disease is not transmitted from prey to predator or conversely, in addition to that both diseases spread within same species by contact between susceptible and infected individuals. Two types of functional response for describing the predation as well as linear incidence for describing transition of diseases are used. The existence, uniqueness, boundedness of the solution and the stability analysis of all possible equilibrium points are studied. The Lyapunov function is used to study the global dynamics of the model. The effect of the disease and harvest on the dynamical of the system is discussed by using numerical simulation.