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

Derivation of the Emergence Probability Approximation. For small mutation likelihood µ, we derive a mathematically explicit version of the approximation (4) for the emergence probability from the main text. As stated in the main text, this approximation is given by the product of three terms: the expected number of secondary, wild-type cases produced during a fade-out, the mean number of individuals infected with mutant virions by an individual initially infected only with the wild-type, and the probability of emergence from an individual infected with a single mutant virion. As noted in the main text, the first term is given by 1 1−Rw . The second term requires more work. To derive an analytic approximation for this term, notice that the mean number of individuals infected with mutant virions by an individual only infected with the wild type equals