Analysis of a Delayed Eco-Epidemiological Pest–Plant Model with Infected Pest

Abstract

This work describes a delayed pest–plant ecological model with infection in the pest population. The interactions between plant and susceptible pest and also between susceptible and infected pest are taken as Holling type II responses. Well-posedness of the system has been discussed. Stability analysis of all equilibria has been performed. The effect of time-delay has been studied, where the delay may be regarded as the incubation period of the infected pest. Existence of a Hopf-bifurcation around interior equilibrium has been established by considering the amount of delay as bifurcation parameter. The length of delay is estimated for which the stability continues to hold. Numerical simulation with a hypothetical set of data has been presented to validate analytical findings.