Discussion on Stability and Hopf-bifurcation of an Infected Prey under Refuge and Predator

Abstract

The paper deals with the case of non-selective predation in a partially infected prey-predator system, where both the susceptible prey and predator follow the law of logistic growth and some preys avoid predation by hiding. The disease-free preys get infected in due course of time by a certain rate. However, the carrying capacity of the predator population is considered proportional to the sum-total of the susceptible and infected prey. The positivity and boundedness of the solutions of the system are studied and the existence of the equilibrium points and stability of the system are analyzed at these points. The effect of the infected prey-refuge on each population density is also discussed. It is observed that a Hopf-bifurcation may occur about the interior equilibrium, where the refuge parameter is considered as the bifurcation parameter. The analytical findings are illustrated through computer simulation using Maple that show the reliability of the model from the ecological point of view.