An eco-epidemiological model with fear effect and hunting cooperation

In this paper, we propose an eco-epidemiological model with disease in the prey population, the model incorporates fear effect of predators on prey and hunting cooperation among predators. We assume that fear can reduce the reproduction rate of the prey population and lower the activity of the prey population, which consequently lowers the disease transmission rate. Mathematical analysis of the model with regard to the non-negativity, boundedness of solutions, stability of equilibria, permanence of the model system are analyzed. The model undergoes backward bifurcation and bistability. We conduct extensive numerical simulations to explore the roles of fear effect, hunting cooperation and other biologically related parameters (e.g. disease transmission rate of prey, death rate of predators), it is found that low levels of fear and hunting cooperation can stabilize the eco-epidemiological system, however, relatively high levels of fear and hunting cooperation can induce limit cycles. Numerical simulations show the occurrence of multiple limit cycles. It is also observed that the system shows limit cycle oscillations for small disease transmission rate/death rate of predators, and the system becomes stable when the disease transmission rate/death rate of predators is high.