Inferring Epidemiological Parameters on the Basis of Allele Frequencies

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Abstract
In this article, I develop a methodology for inferring the transmission rate and reproductive value of an epidemic on the basis of genotype data from a sample of infected hosts. The epidemic is modeled by a birth–death process describing the transmission dynamics in combination with an infinite-allele model describing the evolution of alleles. I provide a recursive formulation for the probability of the allele frequencies in a sample of hosts and a Bayesian framework for estimating transmission rates and reproductive values on the basis of observed allele frequencies. Using the Bayesian method, I reanalyze tuberculosis data from the United States. I estimate a net transmission rate of 0.19/year [0.13, 0.24] and a reproductive value of 1.02 [1.01, 1.04]. I demonstrate that the allele frequency probability under the birth–death model does not follow the well-known Ewens’ sampling formula that holds under Kingman's coalescent.