一类SEIRQ模型的全局稳定性和分岔分析

Global stability and bifurcation analysis of a class of SEIRQ models

研究了一类SEIRQ传染病模型的全局稳定性和分岔现象.基于基本再生数,给出了地方病平衡点的存在条件.讨论了无病平衡点和地方病平衡点的局部稳定性,进一步借助Li-Muldowney的几何方法讨论了地方病平衡点的全局稳定性,利用中心流形定理和正规形理论证明了模型发生了跨临界分岔的现象,展示了传染病在长期传播过程中会逐渐演变成地方传染疾病.最后,对模型进行了数值模拟验证了理论证明的结果.

The global stability and bifurcation of a SEIRQ model of infectious disease are studied.Based on the basic reproduction number,the endemic equilibrium’s existence conditions are derived.The local stability conditions of the endemic and disease-free equilibrium are given.Moreover,the Li-Muldowney geometric technique is applied to study the global stability of endemic disease equilibrium.By the center manifold theorem and normal form theory,it is proved that the transcritical bifurcation occurs,which shows that infectious diseases gradually evolve into endemic diseases during long-term transmission.Finally,the theoretical results are illustrated by numerical simulations.