Trade-off between fear level induced by predator and infection rate among prey species

Abstract

In this article, an eco-epidemic predator–prey model has been considered where the reproduction of susceptible class of prey is assumed to be affected by the induced fear from predators. The positivity and boundedness of solutions along with existence criterion of the non-negative equilibrium points and their local stability analysis have been performed. Hopf-bifurcation analysis with direction around the co-existence equilibrium point is also performed and it is found that the interference competition rate leads the system to Hopf bifurcation and increases the stable co-existence of all the populations. Furthermore, the predator’s induced fear and infection rate among prey species importantly determine the dynamical complexity of the system. Analytical outcomes of the model system suggest that density of infected prey is directly proportional to the level of fear induced by the predator. Extensive numerical simulations have been carried out to validate all the analytical findings. Finally, Hopf-bifurcation curves of co-dimension two are drawn (with special empathises on interference competition rate) to detect various generalised Hopf-bifurcation and zero Hopf-bifurcation points and stability region of the system.