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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 810312, 11 pages
http://dx.doi.org/10.1155/2014/810312
Research Article

Mathematical Analysis of an Epidemic-Species Hybrid Dynamical System

Department of Science and Technology, Guangxi University of Science and Technology, Liuzhou 545006, China

Received 9 March 2014; Revised 30 June 2014; Accepted 20 July 2014; Published 28 August 2014

Academic Editor: Hai-Feng Huo

Copyright © 2014 Jing Hui 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 consider an epidemic-species hybrid dynamical system. The disease is spread among the prey only and the infected prey can reproduce virus. The predator only eats the infected prey. Mathematical analyses are given for the system with regard to the existence of equilibria, local stability, Hopf bifurcation, and the orbital stability of the Hopf bifurcating limit cycle. We further analyse the system under impulsive releasing of virus and predator.