The effect of time delay on the stability of a diffusive eco-epidemiological system

The disease has a vital effect on the dynamical behaviors of predator-prey system in ecology. When disease spreads in the prey population, the infected preys are more likely to be captured by predators. On the other hand, spatial diffusion and gestation delay are ubiquitous in the nature and can generate rich spatiotemporal dynamical behaviors. In this study, a delayed and diffusive predator-prey system with disease in the prey is proposed. First, the existence, uniqueness, positivity and boundedness of solutions are established. Second, the stability condition of constant predator-free equilibrium solution is derived. Third, the stability of constant coexistence equilibrium solution and the existence of Hopf bifurcation are investigated by regarding time delay as the bifurcation parameter. Finally, some numerical simulations and conclusions are given to illustrate the theoretical results. © International Association of Engineers.