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Journal of Applied Mathematics
Volume 2014, Article ID 236208, 9 pages
Research Article

Qualitative Analysis for a Reaction-Diffusion Predator-Prey Model with Disease in the Prey Species

1School of Mathematics & Physics, China University of Geoscience, Wuhan 430074, Hubei Province, China
2Institute of Applied Mathematics and Mechanics, Faculty of Mathematics, Informatics, & Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland

Received 3 February 2014; Accepted 8 April 2014; Published 29 April 2014

Academic Editor: Zhijun Liu

Copyright © 2014 Meihong Qiao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.