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Discrete Dynamics in Nature and Society
Volume 2016 (2016), Article ID 2323752, 10 pages
http://dx.doi.org/10.1155/2016/2323752
Research Article

Positive Solutions of a Diffusive Predator-Prey System including Disease for Prey and Equipped with Dirichlet Boundary Condition

1School of Sciences, Nanchang University, Nanchang 330031, China
2School of Civil Engineering and Architecture, Nanchang University, Nanchang 330031, China
3Numerical Simulation and High-Performance Computing Laboratory, School of Sciences, Nanchang University, Nanchang 330031, China

Received 30 June 2016; Accepted 14 September 2016

Academic Editor: Sanja Konjik

Copyright © 2016 Xiaoqing Wen 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.

Abstract

We study a three-dimensional system of a diffusive predator-prey model including disease spread for prey and with Dirichlet boundary condition and Michaelis-Menten functional response. By semigroup method, we are able to achieve existence of a global solution of this system. Extinction of this system is established by spectral method. By using bifurcation theory and fixed point index theory, we obtain existence and nonexistence of inhomogeneous positive solutions of this system in steady state.