一类非线性时滞 SIR 模型的稳定性与 Hopf 分岔

摘要

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