Dynamical Behaviour of an Infected Predator-Prey Model with Fear Effect

Abstract

In this article, we have presented an infected predator-prey model with Holling type II functional response where the predator population is divided into two sub-classes, namely susceptible and infected due to disease. Here, we have assumed that the fear induced by susceptible and infected predators are of different levels. Well-posedness of the model system along with persistence criterion and the conditions of local stability of each equilibrium point have been established. Direction of Hopf bifurcation near the interior equilibrium point has been investigated. From model analysis, it is observed that fear induced by both susceptible and infected predators jointly determine dynamical complexity of the system. Fear induced by susceptible predators enhances the stable coexistence of the system whereas high amount of fear induced by infected predators destabilizes the system. It is also observed that the ratio of the birth rate of prey and the level of fear induced by both the susceptible and infected predators actively determine the topological behaviour of the system. We have performed comprehensive and meticulous numerical simulations to verify and validate the analytical findings of our model system, and finally, the article is ended up with a conclusion.