Complex dynamics in an eco-epidemiological model with the cost of anti-predator behaviors

In this paper, we investigate the complex dynamics of a predator–prey model with disease in the prey, which is characterized by the reduction of prey growth rate due to the anti-predator behavior. The value of this study lies in two aspects: Mathematically, it provides the existence and the stability of the equilibria and gives the existence of Hopf bifurcation. And epidemiologically, we find that the influence of the fear factor is complex: (i) The level of the population density decreases with the increasing of the fear factor; (ii) the cost of fear can destabilize the stability and benefit the emergency of the periodic behavior; and (iii) the high level of fear can induce the extinction of the predator. These results may enrich the dynamics of the eco-epidemiological systems.