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

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  • Caijuan Yan
  • Jianwen Jia

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 ℛ0 1, we obtain sufficient conditions under which the endemic equilibrium E* 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.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:109372
DOI: 10.1155/2014/109372
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