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.
Meihong Qiao. Anping Liu. Urszula Foryś. "Qualitative Analysis for a Reaction-Diffusion Predator-Prey Model with Disease in the Prey Species." J. Appl. Math. 2014 1 - 9, 2014. https://doi.org/10.1155/2014/236208