一类非线性时滞SIR模型的稳定性与Hopf分岔

Stability and Hopf Bifurcation of Class of Delay SIR Model with Nonlinear Incidence Rate

对于一类具有非线性传染率的时滞SIR模型,首先分析其相应的线性化系统的特征根的分布,论证唯一正平衡点的稳定性,从而获得保持系统稳定的条件,在此基础上,讨论了当时滞参数高于临界点时系统的Hopf分岔.最后进行了数值模拟以证明理论分析的正确性.

The dynamic behavior of a delayed SIR epidemic model system with nonlinear infe rate is investigated. Firstly, the stability of the unique positive equilibrium for the system is ied by analyzing the distribution of characteristic roots of the corresponding linearized sy then the conditions to keep the system stable are obtained. Moreover, it is illustrated that bifurcation will occur when the delay parameter is bigger than a critical value. Finally,the n ical simulation is performed to verify the theoretical result. CtlOUS studstem, Hopf umer