Stochastic effects on endemic infection levels of disseminating versus local contacts

The effects of two levels of mixing on endemic infection levels are shown to differ for identically conformed deterministic compartmental (DC) and stochastic compartmental (SC) models. Both DC and SC models give similar endemic levels when populations are large, immunity is short lived, and mixing is universal. But local transmissions and/or transient immunity decrease overall population infection levels in SC but not in DC models. DC models also fail to detect the greater effects of eliminating disseminating transmissions in comparison to eliminating local transmissions shown by SC models. These differences in model behavior arise because localities that encounter few infections from distant sites and that have stochastically low infection levels have decreased infection rates while localities with stochastically high levels of infection do not decrease the rate at which they lose infection. At the extreme this generates local stochastic die out with subsequent build up of susceptibility in SC but not DC models. This phenomenon should act upon all endemic infections that have changing geographic or social foci of infection. Neither standard epidemiological investigations nor sufficient-component cause models can capture these effects because they occur in the absence of differences between individuals.