Stability Analysis of an SEIS Epidemic ModelWith a Nonlinear Incidence Rate
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摘要: 研究了一类具有非线性传染率的SEIS模型,模型中包含常数输入率、自然死亡率、因病死亡率等.定义了模型的基本再生数R0,并证明了当R0<1时,无病平衡点是全局渐近稳定的.当R0>1时,得到了唯一的地方平衡点是全局渐近稳定的条件.Abstract: An SEIS epidemic model with a nonlinear incidence rate and involving a constant input rate, a natural mortality rate and a mortality rate due to disease, was investigated. Firstly, the basic reproduction number for the model was defined. Then the disease-free equilibrium point was proved to be globally asymptotically stable when R0<1. Finally, the conditions for the theorem that the unique endemic equilibrium point was globally asymptotically stable, were obtained when R0>1.
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