Evolution and emergence of novel human infections

Arinaminpathy, N.; McLean, A. R.

We consider how ongoing pathogen adaptation could be signalled by outbreak sizes, seeking a distribution analogous to figure 1 but with the inclusion of adaptation. Table 1 presents parameters for two different evolutionary scenarios: in the first, 'punctuated' scenario, all adaptations are required together for any increase in reproductive fitness. Thus, relative to the wild-type stage, there is little fitness advantage in partial adaptation, and only the adapted stage has a significantly increased fitness. In the second, 'gradual' scenario, intermediate adaptations confer incremental improvements in fitness. Figure 2 schematically illustrates the progression in fitness from wild-type to adapted stages for both of these scenarios. For illustration figure 3a shows sample time courses of infection for a series of introductions leading to an emergence in the punctuated scenario (movies of simulations leading to these outcomes may be found in the electronic supplementary material). Figure 3b shows the distribution of cluster sizes arising from this series of introductions. In this example, there were 6173 introductions before emergence. The vast majority of introductions go extinct without transmission (i.e. cluster size 1), but there are some instances where limited transmission has occurred. Only 0.16 per cent of outbreaks exceeded two cases. Figure 4 extends these plots to show the general behaviour of cluster size distributions for both punctuated and gradual scenarios. It displays distributions obtained from 25 independent realisations of the process of emergence, with individual distributions distinguished by colour. Insets show distributions for a 10-fold-reduced mutation rate for the final adaptive step. There is a clear variation between the scenarios in the range of cluster sizes accumulated before emergence: the punctuated scenario causes only small clusters, rarely more than four cases large. The gradual scenario shows a broader range of cluster sizes, and such behaviour is due to the state marginally below pandemic capability (R 0 ¼ 0.9). As indicated by figure 1 , such values of R 0 are capable of causing large outbreaks. Indeed, reducing the mutation rate increases the 'dwell time' in this state, and thus the greatest range of cluster sizes before emergence is found in the inset of figure 4, gradual scenario. For comparison, crosses in the plots show the distribution of cluster sizes from case reports of H5N1 avian influenza in Indonesia (World Health Organization). As an aside note that, even after more than 400 cases, the pattern of H5N1 clusters appears compatible with both punctuated and gradual scenarios.