一类SEIRS模型稳定性分析(英文)

The Stability Analysis of an SEIRS Model

建立了一个SEIRS流行病模型,考虑更一般形式的非线性发生率.对恢复类中有时滞和没有时滞的模型进行了比较.结果显示,带有时滞的模型的动力学行为与不带时滞的模型的动力学行为是不同的.对于不带时滞的模型,如果基本再生数小于1,无病平衡点(DFE)是全局渐近稳定的.当基本再生数大于1时,不论免疫期的长短系统都存在唯一的地方病平衡点,并且在一定的条件下是局部渐近稳定的.对于带有时滞的模型,DFE的稳定性依赖于基本再生数和时滞.而且,唯一的地方病平衡点的稳定性也依赖于时滞.另外,通过数值模拟显示,当时滞在一定的范围内时,周期解有可能会出现.

In this paper, nonlinear incidence with a more general form is considered in an SEIRS epidemic model. The model without time delay in the removed class is compared with the model with time delay in the removed class. The result shows that the dynamic behaviors of the model with time delay are different from those of the model without delay. For the model without time delay,the disease free equilibrium（DFE） is globally asymptotically stable when the basic reproduction number is smaller than one. When the basic reproduction number is bigger than one, regardless of the time delay length there exists a unique endemic equilibrium which is locally asymptotically stable under a condition. As for the model with time delay,the stability of the DFE depends on the time delay besides the basic reproduction number. Furthermore, the stability of the unique endemic equilibrium can be obtained under some conditions depending on the time delay. In addition, by numerical simulations, periodic solutions can be found from the endemic equilibrium when the time delay is in some regions.