论文标题
由Preisach操作员建模的个体的疫苗接种和异质行为反应的SIR模型的动力学
Dynamics of SIR model with vaccination and heterogeneous behavioral response of individuals modeled by the Preisach operator
论文作者
论文摘要
我们研究了通过疫苗接种的SIR模型的全球动力学，我们假设个体对流行病的动态的反应不同。它们的异质反应由Preisach滞后算子建模。我们提出了无感染平衡状态全球稳定性的条件。如果这种情况不正确，则该模型具有一组连接的地方性平衡状态，其特征在于受感染和免疫个体的比例不同。在这种情况下，我们表明每个轨迹都会融合到地方性平衡或周期性轨道。在其他自然假设下，排除了周期性的吸引子，我们保证每个轨迹与地方性平衡状态的收敛性。全球稳定性分析使用了与磁滞算子的分支家族相对应的Lyapunov功能系列。
We study global dynamics of an SIR model with vaccination, where we assume that individuals respond differently to dynamics of the epidemic. Their heterogeneous response is modeled by the Preisach hysteresis operator. We present a condition for the global stability of the infection-free equilibrium state. If this condition does not hold true, the model has a connected set of endemic equilibrium states characterized by different proportion of infected and immune individuals. In this case, we show that every trajectory converges either to an endemic equilibrium or to a periodic orbit. Under additional natural assumptions, the periodic attractor is excluded, and we guarantee the convergence of each trajectory to an endemic equilibrium state. The global stability analysis uses a family of Lyapunov functions corresponding to the family of branches of the hysteresis operator.
