Qualitative analysis for a reaction-diffusion predator-prey model with disease in the prey species

Abstract

A diffusive predator-prey system with disease in predator species and no-flux boundary condition is considered. Sufficient conditions which ensure persistence of the system are obtained. Conditions of disease-free ecosystem are also studied. Furthermore, sufficient conditions for global asymptotic stability of the unique positive equilibrium and disease-free equilibrium of the system are derived using the approach of Lyapunov function. © 2014 Meihong Qiao et al.