一类具有媒体报道的 SEIRS 传染病模型的动力学分析

摘要

The dynamics of an SEIRS epidemic model with media coverage was investigated,the basic reproduction number which determines whether the disease is extinct or not was ob-tained.By the linearization and Liapunov function methods,the global stability of the disease-free equilibrium and local stability of the endemic equilibrium were discussed.The permanence of the model was established by applying the theorem of permanence.Finally,numerical simu-lations was employed to verify the theoretical results.%研究一类受媒体报道影响的 SEIRS 传染病模型的动力学行为，寻求决定疾病绝灭与否的基本再生数。利用线性化方法和 Liapunov 函数方法，讨论该模型无病平衡点的全局渐近稳定性和正平衡点的局部渐近稳定性。利用持久性理论证明了模型的持久性。最后通过数值模拟对理论结果进行验证。