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

Our analysis highlights an additional factor, the cross-scale reproductive number α of a mutant virion, previously unrecognized in models neglecting within-host diversity and analyses centered on R 0 for pure infections. Even after the mutant strain has been transmitted, it needs to increase in frequency at the scale of the infected host population (Step 4 in Fig 5) . Specifically, each transmitted mutant virion, on average, needs to replace itself with more than one transmitted mutant virion in the next generation of infected hosts. When this occurs, it sets up a positive feedback along chains of infections: individuals with a higher frequency of the mutant strain tend to infect more individuals, which in turn provides more opportunities to transmit, on average, higher frequencies of the mutant strain to the next generation. Conversely, when this between-generation cross-scale reproductive number α is less than one, the positive feedback leads to lower and lower frequencies of the mutant strain within the infected host population. This positive feedback mechanism is stronger for wider transmission bottlenecks (≥ 5 virions in our numerical explorations), which better preserve the mutant frequency from one host to the next. Interestingly, this 5 virion threshold to define a wider transmission bottleneck is consistent with an earlier modeling study, which found that bottleneck sizes above 5 virions eliminated fitness losses in serial transfers of RNA viruses between cell culture plates [40] .