No abstract

This paper proposes and studies an eco-epidemiological model to describe the dynamic of the spread of a contagious illness of susceptible — infected — susceptible type. This model consists of prey-predator interaction, with the contagious illness in the predator species. It is supposed that, in addition to the existence of harvesting in the prey species and susceptible predator species, the contagious illness is spread only within the predator species through internal contact and external sources, and is not spread to the prey species. The functional response (Lotka-Volterra) is used to describe the Predator Capture. The existence of all fixed points are determined. The bounded and unique nature of the trajectory are proved. The stability (local and global) of all potential fixed points is studied. Finally, a more detailed investigation of the global dynamics of the proposed system is done with the help of numerical simulation.