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Evolutionary stability of minimal mutation rates in an evo-epidemiological model. (English) Zbl 1339.92056
Summary: We consider the evolution of mutation rate in a seasonally forced, deterministic, compartmental epidemiological model with a transmission-virulence trade-off. We model virulence as a quantitative genetic trait in a haploid population and mutation as continuous diffusion in the trait space. There is a mutation rate threshold above which the pathogen cannot invade a wholly susceptible population. The evolutionarily stable (ESS) mutation rate is the one which drives the lowest average density, over the course of one forcing period, of susceptible individuals at steady state. In contrast with earlier eco-evolutionary models in which higher mutation rates allow for better evolutionary tracking of a dynamic environment, numerical calculations suggest that in our model the minimum average susceptible population, and hence the ESS, is achieved by a pathogen strain with zero mutation. We discuss how this result arises within our model and how the model might be modified to obtain a nonzero optimum.
92D15 Problems related to evolution
92D30 Epidemiology
92D10 Genetics and epigenetics
deSolve; diffEq; R
Full Text: DOI
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