Before revision:  Here, we use standard tools from statistical physics to account for this effect, which suggest that the rate of appearance of new cases should be proportional to thesquare of the number of susceptible people in the population, not the first power. We validate this finding with both Monte Carlo (stochastic) and many-compartment differential equation (deterministic) simulations. This leads to quite different predictions of the peak infection rateand final outbreak size, with the second-order model giving milder predictions of each.
After revision:  Here, we use standard tools from statistical physics to account for this effect, which suggest that the rate of appearance of new cases should be proportional to thesquare 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 peak infection rateand final outbreak size, with the second-order model giving milder predictions of each.