Author: Sebastian J. Schreiber; Ruian Ke; Claude Loverdo; Miran Park; Priyanna Ahsan; James O. Lloyd-Smith
Title: Cross-scale dynamics and the evolutionary emergence of infectious diseases Document date: 2016_7_29
ID: hain3be0_103
Snippet: When the outbreak starts, the first individual is infected with wild-type only. When s < 0, the mutation-selection balance can be reached relatively quickly, and for s negative enough, the proportion of mutant is small. So the probability to transmit at least one mutant is roughly equal to the probability to transmit one mutant, which is N exp(τ )r w µ/|s| where r w µ/|s| is the proportion of the mutant type, and exp(τ ) is its relative trans.....
Document: When the outbreak starts, the first individual is infected with wild-type only. When s < 0, the mutation-selection balance can be reached relatively quickly, and for s negative enough, the proportion of mutant is small. So the probability to transmit at least one mutant is roughly equal to the probability to transmit one mutant, which is N exp(τ )r w µ/|s| where r w µ/|s| is the proportion of the mutant type, and exp(τ ) is its relative transmissibility. Then, if s is small enough, then the reproductive number of an individual with a mixed transmission is close to R w of the wild-type. Thus, the number of transmissions in a wild-type outbreak can be used (R w /(1 − R w )). For an individual infected with a mixed infection, what will lead to emergence are the contacts for which only the mutant is transmitted. The number of such contacts is:
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