Hopf bifurcation of a delayed epidemic model with information variable and limited medical resources. (English) Zbl 1406.92637

Yan, Caijuan; Jia, Jianwen

Abstr. Appl. Anal. 2014, Article ID 109372, 11 p. (2014).

Summary: 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 \(\mathcal{R}_0 < 1\), we discuss the global asymptotical stability of the disease-free equilibrium by constructing a Lyapunov functional. If \(\mathcal{R}_0 > 1\), 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.

MSC:

92D30	Epidemiology
92C60	Medical epidemiology
34C23	Bifurcation theory for ordinary differential equations
34D20	Stability of solutions to ordinary differential equations

Keywords:

Hopf bifurcation; delayed epidemic model; limited medical resources; stability

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