Effects of incubation and gestation periods in a prey–predator model with infection in prey

Abstract

In this paper, we study a wide spectrum of dynamical features of a prey–predator model with infection in prey population only. In the model formulation, we consider nonlinear incidence for infection transmission and Holling type II as response function of predator. We analyze the model for local stability and Hopf bifurcation, and the theoretical results are validated and extrapolated by numerical simulations. Also, we perform sensitivity analysis to explore the significance of the crucial parameters influencing the densities of prey and predator populations. Our numerical results show that disease persists in the system even if the basic reproduction number is below unity. The rates of predation on susceptible and infected prey populations are shown to dramatically change the behavior of eco-epidemiological system. We extend our model by considering the fact that the newly infected prey becomes productively infectious after the effective contact between susceptible and infectious preys, and some time lag is involved in this biological process; also the conversion process conceals some time. We analyze our eco-epidemiological model with two time delays (incubation delay and predator’s gestation delay) for stability and bifurcation. From numerical simulations, we observe that both the delay parameters substantially affect the stable configuration of the system.