Susceptibility governs the dynamics of contagion. The classical SIR model is one of the simplest compartmental models of contagion spread, assuming a single shared susceptibility level. However, variation in susceptibility over a population can fundamentally affect the dynamics of contagion and thus the ultimate outcome of a pandemic. We develop mathematical machinery which explicitly considers susceptibility variation, illuminates how the susceptibility distribution is sculpted by contagion, and thence how such variation affects the SIR differential questions that govern contagion. Our methods allow us to derive closed form expressions for herd immunity thresholds as a function of initial susceptibility distributions and suggests an intuitively satisfying approach to inoculation when only a fraction of the population is accessible to such intervention. Of particular interest, if we assume static susceptibility of individuals in the susceptible pool, ignoring susceptibility diversity {\em always} results in overestimation of the herd immunity threshold and that difference can be dramatic. Therefore, we should develop robust measures of susceptibility variation as part of public health strategies for handling pandemics.

中文翻译：

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人口易感性变化及其对传染动态的影响

易感性控制着传染的动态。经典的 SIR 模型是最简单的传染病传播分区模型之一，假设有一个共享的易感性水平。然而，人群易感性的变化可以从根本上影响传染的动态，从而影响大流行的最终结果。我们开发了明确考虑敏感性变化的数学机制，阐明了传染性如何塑造敏感性分布，以及这种变化如何影响控制传染性的 SIR 微分问题。我们的方法允许我们推导出作为初始易感性分布函数的群体免疫阈值的封闭形式表达式，并在只有一小部分人口可进行此类干预时提出一种直观令人满意的接种方法。特别有趣的是，如果我们假设易感人群中个体的静态易感性，忽略易感性多样性 {\em always} 会导致高估群体免疫阈值，并且这种差异可能是巨大的。因此，我们应该制定强有力的易感性变异措施，作为应对大流行的公共卫生战略的一部分。忽略易感性多样性 {\em always} 会导致高估群体免疫阈值，并且这种差异可能是巨大的。因此，我们应该制定强有力的易感性变异措施，作为应对大流行的公共卫生战略的一部分。忽略易感性多样性 {\em always} 会导致高估群体免疫阈值，并且这种差异可能是巨大的。因此，我们应该制定强有力的易感性变异措施，作为应对大流行的公共卫生战略的一部分。