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.
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 infection susceptibility. We 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. Intriguingly, 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 often tend 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.
R
disease
infection
R
leads to the natural emergence of a power law in the
strongly influences the rate of infection, while the infection process simultaneously sculpts the susceptibility distribution. These joint dynamics influence the
R
(\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
and are, in turn, influenced by the shape of the initial variability. Intriguingly, 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 often tend towards these "eigen-distributions" through the process of contagion
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epidemic