Heterogeneity in susceptibility dictates the order of epidemiological models
The fundamental models of epidemiology describe the progression of an infectious disease through a population using compartmentalized differential equations, but do not incorporate population-level heterogeneity in disease susceptibility. We show that variation leads to the natural emergence of a power law in the force of infection ($\beta I S^p$), where the order $p$ is a simple function of the distribution shape. $p$ is significantly greater than one for reasonable variances, suggesting that conventional epidemic models make extreme assumptions about the absence of variance in susceptibility. The power-law behavior fundamentally alters predictions of the long-term infection rate, and suggests that first-order models that are parameterized in the exponential-like phase may systematically and significantly over-estimate the final severity of the outbreak.
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