具有媒体效应和接种的传染病模型的稳定性分析

摘要

讨论了一类具有媒体效应和接种的传染病模型。首先分析了各平衡点存在的充分条件，然后应用Hurwitz判据得到了平衡点的局部渐近稳定性，通过分析极限环的存在唯一性得到了平衡点的全局渐近稳定性，最后探讨了接种率和媒体效应对疾病的防控作用。%A class of infectious disease model with media effects and vaccination is discussed. The sufficient conditions for the existence of the equilibrium points are analyzed,and the local asymptotic stability of the equilibrium point is obtained by using the Hurwitz criterion. The global asymptotic stability of the equilibrium point is obtained by analyzing the existence and uniqueness of the limit cycle.