Study of delay induced eco-epidemiological model incorporating a prey refuge

Abstract

The present study deals with the dynamical response of an eco-epidemiological model consisting of prey and predator species having infection in prey population. The inclusion of prey refugia is taken into account to avoid predator attack. The entire prey population is divided into two parts: healthy prey  which are capable of reproducing  following the logistic law and infected prey which is removed by predation or death before having the possibility of reproducing. This dynamical system assumes that predators form a dense colony or school in a single (possibly moving) location to encounter a prey and due to that an encounter between the prey and a single predator is immediately converted into an encounter between the prey and all the predators. This special type of interaction is approximated by a response function which is ratio dependent at high predator density. The dynamical responses in terms of boundedness, the local stability and bifurcation are studied in detail. Numerical simulations are performed at the end in order to exhibit the dynamical behavior of the present system for the occurrence of limit cycle and bifurcation based on the analytical results and choice of parameters involved in it.