In the special case N?? and S=N?1 it is possible to calculate the probability of emergence per introduction into the human host population, given the evolutionary course of the pathogen, and the mutation rate with which the pathogen adapts. Our derivations start with assuming one homogeneous human host population of infinite size. This assumption can be easily relaxed as we show later. To calculate the probability of emergence, we define next event probabilities of infection p i , mutation m i , and recovery r i for each individual infected host, therefore the probabilities for what type of event will come next for each infectious host are