Evolution and emergence of novel human infections

Arinaminpathy, N.; McLean, A. R.

If a pathogen causes many hundreds of cases yet fails to show any sustained human transmission, does this mean that it is incapable of adapting for human transmission? More specifically, how many 'failed' human cases should occur for such a conclusion? Table 1 . Parameters for punctuated and gradual scenarios, assuming four adaptive stages. For instance, in the punctuated scenario, the wild-type pathogen has R 0 ¼ 0 in humans. After acquiring an adaptation, it has R 0 ¼ 0.1 and so forth. Here, an adapted pathogen has R 0 ¼ 2, and a mutation rate M ¼ 0.1 is associated with all adaptive stages. For a given series of reproductive numbers and mutation rates, it is possible to calculate the probability p e of emergence, per introduction, using the theory of multi-type branching processes (Athreya & Ney 1972) . If there are insurmountable biological barriers to adaptation, this is equivalent to p e ¼ 0. Thus, repeated introductions into the human population are akin to a series of coin tosses, where the probability of 'heads' (corresponding to emergence) per toss is p e . The number of coin tosses before the first head follows a negative binomial distribution. Assume an observation that N tosses have yielded only tails, corresponding to a series of failed introductions. The probability of such an outcome is at least 50 per cent as long as p e , 1 À 2 ðÀ1=NÞ ;