A simple method of estimating rabies outbreak sizes from phylogenies

The ability to estimate the size of a disease outbreak is beneficial both for coordinating an outbreak response and for retrospectively evaluating the effectiveness of response measures and surveillance. Methods such as seroprevalence surveys and epidemiological modelling can be used for this purpose, but are not suitable for every outbreak. We develop a simple formula to estimate the proportion of outbreak cases sequenced, using only the per-generation substitution rate and the length of a phylogenetic tree. This proportion can then be used to estimate the outbreak size. We validate this method using subsampled data from fully observed simulated outbreaks, and then apply it to an ongoing rabies outbreak in the Philippines. We find that this method produces accurate estimates of outbreak size and can be applied to outbreaks with substitution rates and R0 values within the estimated range for rabies. We estimated that approximately 19% of cases from the outbreak in the Philippines had been sequenced, suggesting better than average case detection, with a resulting outbreak size estimate consistent with previous analyses. With this method and the associated R package POSER (https://github.com/RowanDurrant/poser), we aim to make rabies outbreak size estimation more accessible, but further work is required to improve its applicability to other diseases.