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

机译：具有信息变量和有限医学资源的时滞流行病模型的H​​opf分支。

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摘要

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 ratioℛ0<1, we discuss the global asymptotical stability of the disease-free equilibrium by constructing a Lyapunov functional. Ifℛ0>1, we obtain sufficient conditions under which the endemic equilibriumE*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.
机译：我们考虑了SIR流行病模型，其中在没有疾病的情况下，人口增长受逻辑增长的影响。我们得到了具有信息变量和有限医疗资源的时滞流行病模型的霍普夫分支的条件。通过分析相应的特征方程，讨论了地方平衡和无病平衡的局部稳定性。如果基本繁殖率ℛ0<1，我们通过构造一个Lyapunov泛函讨论无病平衡的全局渐近稳定性。如果ℛ0> 1，我们得到系统的地方均衡E *局部渐近稳定的充分条件。并且我们还讨论了Hopf分叉的稳定性和方向。进行数值模拟以解释数学结论。

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