Cross-scale dynamics and the evolutionary emergence of infectious diseases

Sebastian J. Schreiber; Ruian Ke; Claude Loverdo; Miran Park; Priyanna Ahsan; James O. Lloyd-Smith

Second, the mutant strain must be transmitted successfully to susceptible individuals -the second term I w→m of our approximation (4) . For an individual initially infected only with the wild-type strain, I w→m equals the product of the contact rate, the infection duration, and the likelihood that a mutant virion is transmitted during a contact event, averaged over the full course of infection (Appendix). The likelihood of transmitting mutant virions on the t th day of infection is proportional to the product of the transmission bottleneck width (N ), the within-host frequency of the mutant strain, and the transmissibility b m of the mutant strain. This highlights an important distinction between short-term and long-term infections. For short-term infections where sT is small, there is insufficient time for the frequency of mutants to rise within a host, so transmission events with mutant virions are rare (< 1/1, 000 for all black contour lines in Fig 2A,B ). This is a key obstacle to evolutionary emergence in short-term infections. In contrast, for long-term infections where the mutant strain has a substantial within-host selective advantage, the mutant strain is transmitted frequently (e.g. the expected number of events > 1 for some contours in Fig 2C,D) .