一类具有常数输入率的有差异的两子群间的SIRS模型
An SIRS Model with Constant Immigration Rate Between Two Discrepant Subgroups
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摘要: 建立并分析了一类总人口变动的包含具有差异性两子群的单种群的SIRS传染病模型.当基本再生率R_0≤1时,系统仅存在无病平衡点,且它是全局渐近稳定的.当R_0 >1时,存在唯一的地方病平衡点,并且它存在即局部渐近稳定.通过Lyapunov函数法建立了地方病平衡点全局渐近稳定的充分条件.Abstract: An SIRS epidemiological model for a single species population with varying size and two discrepant sub-groups is formulated and analyzed.If the basic reproduction rate R_0≤ 1, only the disease-free equilibrium exists, which proves to be globally asymptotically stable.There exists a unique endemic equilibrium if R_0 > 1 and it is local-ly asymptotically stable whenever it exists.Sufficient conditions are obtained for global asymptotic stability of the endemic equilibrium via the method of Lyapunov functions.
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