A Model Based Theoretical Study on Cannibalistic Prey–Predator System with Disease in Both Populations

Abstract

In this paper, we propose a prey–predator system with disease in both the prey and predator populations. We also consider that the predator population is cannibalistic in nature and the disease spread in the predator population through cannibalism. Local stability of the system around the biologically feasible equilibria are studied. We also analyze the community structure of the system in terms of ecological and disease basic reproduction numbers. We observe that cannibalism in predator population stabilized the prey–predator oscillations. It is also observed that cannibalism can control the disease in the system. The existence of Hopf bifurcation is investigated by choosing the appropriate bifurcation parameter, and also derive the conditions for the permanence of the system. Furthermore, 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. Finally extensive numerical experiments are performed to validate analytical findings.