Cannibalistic Predator–Prey Model with Disease in Predator — A Delay Model

Abstract

In this paper, we propose and analyze a cannibalistic predator–prey model with a transmissible disease in the predator population. The disease can be transmitted through contacts with infected individuals as well as the cannibalism of an infected predator. We also consider incubation delay in disease transmission, where the incubation period represents the time in which the infectious agent develops in the host. Local stability analysis of the system around the biologically feasible equilibria is studied. Bifurcation analysis of the system around interior equilibrium is also studied. Applying the normal form theory and central manifold theorem, the direction of Hopf bifurcation, the stability and the period of bifurcating periodic solutions are derived. Under appropriate conditions, the permanence of the system with time delay is proved. Our results suggest that incubation delay destabilizes the system and can produce chaos. We also observe that cannibalism can control disease and population oscillations. Extensive numerical simulations are performed to support our analytical results.