带有垂直传播和接种疫苗的SEIRS传染病模型的全局稳定性
Global Stability of an SEIRS Epidemic Model with Vertical Transmission and Vaccination
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摘要: 建立了一个考虑了疾病的水平传播和垂直传播以及接种疫苗等因素的传染病模型,通过排除周期解、同宿轨和异宿环的存在来研究了模型的全局稳定性,最后证明了系统的全局动力学特性完全由基本再生数Ro所确定:当Ro≤1时,无病平衡点是全局渐进稳定的;当Ro＞1时,地方病平衡点是全局渐进稳定的.Abstract: In this paper,by ruling out the presence of periodic solutions,homoclinic orbits and heteroclinic cycles,we study the global stability of an SEIRS epidemic model which incorporates exponential growth,horizontal transmission,vertical transmission,standard incidence and vaccination.It is shown that the global dynamics are completely determined by the basic reproduction number Ro.If Ro≤1,the disease-free equilibrium is globally asymptotically stable;whereas if Ro＞1,the unique endemic equilibrium is globally asymptotically stable.
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