The Dynamics of an SIS Epidemic Disease with Contact and External Source

Abstract

In this paper, we discuss the dynamical behavior of eco-epidemiological mathematical model consisting of prey-predator model involving SIS infectious disease in prey population, is proposed and analyzed. This disease passed from a prey to predator through attacking of predator to prey. It is assumed that the disease transmitted within the same species by contact between susceptible individuals and infected individuals, in additional to the external sources from the environment. The existence, uniqueness and boundedness of the solution of the system are studied. The local and global stability conditions of all possible equilibrium points are established. Finally, some numerical simulations are given to illustrate the analytical results.

Keywords: prey-predator model, SIS epidemics disease, stability analysis, Lyapunov function.