A predator–prey mathematical model with both the populations affected by diseases

Abstract

A prey–predator model with disease in both the population is proposed and analyzed. Local stability analysis of biologically feasible equilibrium points is worked out with help of ecological as well as disease basic reproduction numbers. We also explain the community composition of ecosystem by basic reproduction numbers. It is shown that the system is globally stable around the interior equilibrium point under certain parametric conditions. Moreover, the system is persistent under some feasible parametric conditions. Our analysis reveals that force of infection and predation rate are the key parameters on the dynamics of the system. Extensive numerical experiments with hypothetical set of parameters are carried out to substantiate our analytical findings. The oscillatory coexistence of the species which is very common in nature is observed for predator disease free system. The introduction of disease in the predator population enhances the extinction of predator population. We also observe that the system will be disease free and all population will persist through proper predational strategies.