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

Finally, even if the mutant strain is successfully transmitted, an individual infected with the mutant strain needs to give rise to a major outbreak which occurs with probability P m , see equation (4) . This requires the mutant strain to rise in frequency in the infected host population. A mean field analysis for larger bottleneck sizes (N > 5 in the simulations) reveals that mutant frequency initially grows geometrically by the cross-scale reproductive number α of a mutant virion-the number of mutant virions, on average, transmitted by an individual initially infected with a single mutant virion and N − 1 wild type virions (Appendix). If this cross-scale reproductive number is greater than one, then each mutant virion replaces itself with more than one mutant virion in the next generation of infection, and the frequency of mutant virions increases in the infected host population. If the cross-scale reproductive number α is less than one, the frequency of mutants decreases, thereby hindering evolutionary emergence.