Stability and bifurcation analysis of prey-predator model with SIS type of disease and anti-predator property

Abstract

A prey-predator model involving anti-predator behavior and fear of predation with disease in a predator is proposed and studied. The main objective of this study is to find out the influence of anti-predator and fear on the population dynamics of the model in the presence of disease. It is assumed that the disease in the predator is of the SIS type. For this purpose, a mathematical model with a Holling- type II functional response was proposed and analyzed. The existence conditions and stability of different equilibrium points for the model were analyzed to determine the qualitative behavior of the model. Investigations of local bifurcations had been conducted. It can be shown that the results of numerical simulations are consistent with analytical results.