DYNAMICAL STUDY OF FEAR EFFECT IN PREY–PREDATOR MODEL WITH DISEASE IN PREDATOR

Abstract

In predator–prey system, the impact of predation fear on the prey population has received significant attention from researchers recently. A predator–prey community with infected predator in presence of predation fear has not yet been studied. We model a predator–prey system with disease transmission in predator and predator-induced fear in prey. We consider two crucial mechanisms where fear of prey can be detrimental to the prey due to low reproduction, and disease in predator can be beneficial to the prey due to low predation risk. In this study, we investigate the simultaneous effect of disease transmission and the cost of predation fear on the system dynamics. We study the dynamics of such system around the equilibrium points by stability and bifurcation analysis. Analytical results establish the occurrence of transcritical and Hopf bifurcation into the system dynamics. Numerical results reveal that high strength of predation fear and disease transmissions can stabilize the system by excluding oscillations. We show that the increased strength of disease transmission control or extinction of the predator yet permits the prey species to recuperate. The study indicates that infectious diseases may act as a biological control to control undesirable species. In the presence of fear, the half-saturation constant plays a vital role in shrinking or expanding the oscillatory region. Also, we identify a scenario in which the disease transmission rate produces a bubbling effect around an endemic equilibrium. We validate our analytical findings through numerical simulations.