Conversely, a novel pathogen of zoonotic origin emerges if it is sufficiently adapted for human transmission and begins to spread in a self-sustaining way. Formally, in an unlimited host population the cumulative number of infectious hosts is unbounded as time goes to infinity. Computationally we use a threshold of I 3~1 00 infectious hosts with the fully adapted strain to distinguish between emergence and extinction. This threshold ensures a probability of extinction less than (1=R 3 ) I3~7 :9 Ã 10 {31 [16] . Therefore, the number of falsely identified emergences, which would truly be extinctions, is negligibly small. Moreover, these arbitrarily small probabilities ensure that our simulation results are insensitive to the precise choice of threshold used. In situations where the host population is very small we relax our emergence threshold to smaller numbers of infectious hosts as some population sizes are below 100.