  Most infectious diseases including more than half of known human pathogens
are not restricted to just one host, yet much of the mathematical modeling of
infections has been limited to a single species. We investigate consequences of
a single epidemic propagating in multiple species and compare and contrast it
with the endemic steady state of the disease. We use the two-species
Susceptible-Infected-Recovered (SIR) model to calculate the severity of
post-epidemic collapses in populations of two host species as a function of
their initial population sizes, the times individuals remain infectious, and
the matrix of infection rates. We derive the criteria for a very large,
extinction-level, population collapse in one or both of the species. The main
conclusion of our study is that a single epidemic could drive a species with
high mortality rate to local or even global extinction provided that it is
co-infected with an abundant species. Such collapse-driven extinctions depend
on factors different than those in the endemic steady state of the disease.
