Abstract:
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Branching processes have historically been used to provide a generating mechanism for the transmission of infectious disease within a large population. For example, in Farrington et al. (2003), the authors derive the unconditional likelihood for the offspring in order to estimate the effective reproduction number. We extend their method to include additional covariates in order to estimate the probability of transmission from individual to individual within a transmission tree. As motivation, we analyze the transmission of Tuberculosis among Maryland residents in the mid 2000s. In the data there are over 150 clusters of individuals with related mutations of TB, ranging from clusters of size 1 to size 25. We are especially interested in estimating the effect of the covariate smear status (+/-) on the forward transmission probability of the disease. To aid in our analysis, we develop an R package to simulate, estimate, and visualize parameters related to disease transmission in moderately sized clusters of individuals.
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