具有时滞影响的SIRC传染病模型的Hopf分支分析

Hopf bifurcation of a SIRC epidemic model with delay

讨论了一个具有时滞影响的关于流感A的SIRC传染病模型。首先求得基本再生数R0,研究了模型平衡点的存在性及稳定性;其次证明了时滞可以导致系统Hopf分支的产生;然后,利用中心流形定理和规范型理论讨论了分支方向和周期解的稳定性;最后给出了数值模拟。

This article concerns a SIRC model for Influenza A with time delay.The basic reproduction number R0 is calculated.For the model without delay,we demonstrate the conditions for global stability of equilibria.And we show that the delay can only change the stability of the endemic equilibrium and lead to the existence of Hopf bifurcation.By applying the center manifold theorem,normal form theory,we also derive some explicit formulae determining the bifurcation direction and the stability of the bifurcated periodic solutions.Finally,numerical simulation is given to support our results.