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Abstract and Applied Analysis
Volume 2014, Article ID 109372, 11 pages
http://dx.doi.org/10.1155/2014/109372
Research Article

Hopf Bifurcation of a Delayed Epidemic Model with Information Variable and Limited Medical Resources

School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, China

Received 7 January 2014; Revised 4 March 2014; Accepted 10 March 2014; Published 9 April 2014

Academic Editor: Kaifa Wang

Copyright © 2014 Caijuan Yan and Jianwen Jia. 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 SIR epidemic model in which population growth is subject to logistic growth in absence of disease. We get the condition for Hopf bifurcation of a delayed epidemic model with information variable and limited medical resources. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease-free equilibrium is discussed. If the basic reproduction ratio , we discuss the global asymptotical stability of the disease-free equilibrium by constructing a Lyapunov functional. If , we obtain sufficient conditions under which the endemic equilibrium of system is locally asymptotically stable. And we also have discussed the stability and direction of Hopf bifurcations. Numerical simulations are carried out to explain the mathematical conclusions.