Transitions in the two-pathogen stochastic models.

The prevalence of uninfected host is J∅, the prevalence of each class of singly infected hosts is Ji (for i∈[1,2]), and the prevalence of coinfected host is J1,2. The net force of infection of pathogen i is Fi = βiIi/N = βi(Ji+J1,2)/N (note the scaling by the population size N relative to the forces of infection as used in the deterministic version of the model). To ensure a constant host population size, we have made the simplifying assumption that removal and replacement occur simultaneously; this has no effect on our qualitative results.