对干预政策具有异质响应的SIR模型的动力学
Dynamics of SIR model with heterogeneous response to intervention policy
摘要：
我们研究动态的一个变种的SIR模型，在那里我们假设个人的动态响应不同的流行病。它们的非均质响应由Preisach滞后算子建模。响应的异质性程度通过相应分布的方差$σ^2$（Preisach密度函数）测量。该模型具有一个连续的地方病平衡态，其特征在于不同比例的易感，感染和恢复人口。我们考虑如何的极限点的流行病轨迹和感染高峰沿这条轨迹取决于$σ$。将异质模型与具有对应于$σ=0$的理想均匀响应的切换模型进行比较。
英文摘要：
We study dynamics of a variant of the SIR the model, where we assume that individuals respond differently to dynamics of the epidemic. Their heterogeneous response is modeled by the Preisach hysteresis operator. The degree of heterogeneity of the response is measured by the variance $σ^2$ of the corresponding distribution (the Preisach density function). The proposed model has a continuum of endemic equilibrium states characterized by different proportions of susceptible, infected and recovered populations. We consider how the limit point of the epidemic trajectory and the infection peak along this trajectory depend on $σ$. The heterogeneous model is compared to the the switched model with an ideally uniform response corresponding to $σ=0$.
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