Stability and bifurcation analysis of an eco-epidemiological model with prey refuge

Abstract

In this paper, we propose and analyse a predator-prey model with disease in prey. We assume that a portion of healthy prey takes refuge to avoid predation. We find the biologically feasible equilibrium points and their stability criteria by using linearization technique. We also perform Hopf bifurcation analysis around the co-existing equilibrium point. We use substantial numerical simulation to verify our theoretical results and to investigate rich dynamics that are not possible to achieve analytically. We illustrate rich dynamics such as Hopf bifurcation, chaos, bistability, and others using one and two parameter bifurcation diagrams. We find that disease invasion in prey can produce chaos by inducing period-doubling bifurcation, but refuge can reduce chaos by causing period-halving bifurcation. We also observe that refuge can reduce the prevalence of disease in the prey population.