The dynamics and analysis of an SIS disease of a stage-structured prey-predator model with a prey refuge

Abstract

In this paper, the dynamical behaviour of an {epidemiological system} has been investigated. A stage-structured prey-predator model includes harvest and refuge for only prey, the disease of type (SIS) is just in the immature of the prey and the disease is spread by contact and by external source has been studied. The transmission of infectious diseases in the prey populations has been described by the linear type. While Lotka-Volterra functional response is used to describe the predation process of the whole prey population. This model has been represented by a set of nonlinear differential equations. The solution's existence, uniqueness and boundedness have been studied. "The local and global stability conditions of all the equilibrium points" have been confirmed. As a final point, numerical simulation has been used to study the global dynamics of the model.