Complex Dynamics in a Predator–Prey Model with Fear Affected Transmission

Cooperation during hunting is one of the generic strategies adopted by the predators that creates fear among their prey. In this study, an eco-epidemiological model is proposed by incorporating the cost of fear that significantly impacts prey reproduction and the rate of disease transmission. The existence and local stability of all biologically feasible equilibrium points of the model are presented. Effects of various important factors viz., hunting cooperation, predation rate, disease transmission rate and prey reproduction rate on the system dynamics are explored. Codimension one and codimension two bifurcations, including Chenciner and Fold-Neimark Sacker bifurcation, are obtained. Homoclinic orbits initiating from a Bogdanov-Takens bifurcation point are observed. Furthermore, a catastrophic shift is observed while varying the death rate of infected prey and a bistability region for the same parameter is obtained. Finally, mortality and disease induced positive Hydra effect are observed in the proposed model.