The fundamental models of epidemiology describe the progression of an infectious disease through a population using compartmentalized differential equations, but typically do not incorporate population-level heterogeneity in infection susceptibility. Here we combine a generalized analytical framework of contagion with computational models of epidemic dynamics to show that variation strongly influences the rate of infection, while the infection process simultaneously sculpts the susceptibility distribution. These joint dynamics influence the force of infection and are, in turn, influenced by the shape of the initial variability. We find that certain susceptibility distributions (the exponential and the gamma) are unchanged through the course of the outbreak, and lead naturally to power-law behavior in the force of infection; other distributions are often sculpted towards these “eigen-distributions” through the process of contagion. The power-law behavior fundamentally alters predictions of the long-term infection rate, and suggests that first-order epidemic models that are parameterized in the exponential-like phase may systematically and significantly over-estimate the final severity of the outbreak. In summary, our study suggests the need to examine the shape of susceptibility in natural populations as part of efforts to improve prediction models and to prioritize interventions that leverage heterogeneity to mitigate against spread.

流行病学的基本模型使用分区微分方程描述传染病在人群中的进展，但通常不包括感染易感性的人群水平异质性。在这里，我们将传染的广义分析框架与流行动力学的计算模型相结合，以表明变异强烈影响感染率，而感染过程同时塑造了易感性分布。这些关节动力学影响感染力，反过来又受到初始变异性形状的影响。我们发现某些易感性分布（指数和伽马）在爆发过程中没有变化，并且在感染力下自然导致幂律行为；其他分布通常通过传染过程被塑造成这些“特征分布”。幂律行为从根本上改变了对长期感染率的预测，并表明在指数阶段参数化的一阶流行模型可能会系统地、显着地高估疫情的最终严重程度。总而言之，我们的研究表明，需要检查自然种群的易感性形状，作为改进预测模型和优先考虑利用异质性来减轻传播的干预措施的一部分。并表明在指数阶段参数化的一阶流行病模型可能会系统地、显着地高估疫情的最终严重程度。总而言之，我们的研究表明，需要检查自然种群的易感性形状，作为改进预测模型和优先考虑利用异质性来减轻传播的干预措施的一部分。并表明在指数阶段参数化的一阶流行病模型可能会系统地、显着地高估疫情的最终严重程度。总而言之，我们的研究表明，需要检查自然种群的易感性形状，作为改进预测模型和优先考虑利用异质性来减轻传播的干预措施的一部分。