具有非线性发生率的 SIR 模型中过冲的上界
Upper Bounds on Overshoot in SIR Models with Nonlinear Incidence
AI总结：
本文将 SIR 模型流行病过冲的上界分析扩展到非线性发生率，给出解析流程，并通过示例和接触网络数值实验说明更陡发生率与更高接触异质性会扩大过冲构成显著公共卫生危害的疾病范围。
摘要：
我们扩展了 SIR 模型中流行病过冲上界的计算，以纳入非线性发生率。我们阐述了对易感者数量的非线性函数进行解析计算的一般步骤和限制条件。我们通过若干示例演示了该流程，并通过数值方法研究了当非线性发生率以接触网络上的流行病动力学形式出现时，过冲的上界会发生什么。我们发现，更陡峭的发生率项和更大的接触异质性都会扩大可传播疾病的范围，在这些疾病中，过冲仍是相对较大的公共卫生危害。
英文摘要：
We expand the calculation of the upper bound on epidemic overshoot in SIR models to account for nonlinear incidence. We lay out the general procedure and restrictions to perform the calculation analytically for nonlinear functions in the number of susceptibles. We demonstrate the procedure by working through several examples and also numerically study what happens to the upper bound on overshoot when nonlinear incidence manifests in the form of epidemic dynamics over a contact network. We find that both steeper incidence terms and larger contact heterogeneity can increase the range of communicable diseases at which the overshoot remains a relatively large public health hazard.
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