Papers › Heterogeneity in susceptibility dictates the order of epidemiological models
Heterogeneity in susceptibility dictates the order of epidemiological models
Christopher Rose, Andrew J. Medford, C. Franklin Goldsmith, Tejs Vegge, Joshua S. Weitz, Andrew A. Peterson
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 (βI Sᵖ), 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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