Bifurcation and onset of chaos in an eco-epidemiological system with the influence of time delay

Abstract

In the present article, we investigated a delay-based eco-epidemic prey–predator system in the presence of environmental fluctuations where predators engage with susceptible and infected prey, adopting Holling type II and ratio-dependent functional responses, respectively. During the study of the considered model, we identify each potential equilibrium point and its local stability criterion. The basic reproduction number has been computed, and the backward bifurcation about the disease-free equilibrium point was analyzed. The article illustrates Hopf bifurcation, global stability at the endemic equilibrium point, and their graphical depiction. We look over the variations in the dynamics of non-delay, delayed, and stochastic systems, revealing that a fixed level of temporal delay results in chaotic motion for the increasing strength of the saturation constant yet is potentially controlled by the predator growth rate. To study the dynamic behavior of the solution of the considered system and verify all theoretical results, we use numerical simulation and minutely analyze the influence of model parameters on the solution of the considered system. The stochastic transition is studied by varying the strength of stochastic fluctuation and the effect of delay.