Global dynamics of an SEIR epidemic model with vertical transmission
Global dynamics of an SEIR epidemic model with vertical transmission
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DOI：
10.1137/s0036139999359860
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发表时间：
2001-10-02
影响因子：
1.9
通讯作者：
Wang, LC
中科院分区：
文献类型：
--
作者：
Li, MY;Smith, HL;Wang, LC
我们研究一种传染病的人口模型，该传染病通过水平和垂直传播在宿主人群中传播。假设总宿主人口具有恒定密度，并且发生率项具有双线性质量作用形式。我们证明，全局动态完全由基本再生数 R-0(p,q) 决定，其中 p 和 q 分别是暴露类别和感染类别中受感染新生儿的比例。如果 R-0 (p,q) 小于或等于 1，则无病平衡是全局稳定的，并且疾病总是会消失。如果 R-0(p,q) > 1，则存在独特的地方病平衡，并且在可行区域内部全局稳定，并且如果疾病最初存在，则该疾病将持续处于地方病平衡状态。还分析了垂直传播对基本再生数的贡献。
We study a population model for an infectious disease that spreads in the host population through both horizontal and vertical transmission. The total host population is assumed to have constant density and the incidence term is of the bilinear mass-action form. We prove that the global dynamics are completely determined by the basic reproduction number R-0(p,q), where p and q are fractions of infected newborns from the exposed and infectious classes, respectively. If R-0 (p,q)less than or equal to1, the disease-free equilibrium is globally stable and the disease always dies out. If R-0(p,q) > 1, a unique endemic equilibrium exists and is globally stable in the interior of the feasible region, and the disease persists at an endemic equilibrium state if it initially exists. The contribution of the vertical transmission to the basic reproduction number is also analyzed.