Using an epidemiological model for phylogenetic inference reveals density dependence in HIV transmission

The control, prediction, and understanding of epidemiological processes require insight into how infectious pathogens transmit in a population. The chain of transmission can in principle be reconstructed with phylogenetic methods which analyze the evolutionary history using pathogen sequence data. The quality of the reconstruction, however, crucially depends on the underlying epidemiological model used in phylogenetic inference. Until now, only simple epidemiological models have been used, which make limiting assumptions such as constant rate parameters, infinite total population size, or deterministically changing population size of infected individuals. Here, we present a novel phylogenetic method to infer parameters based on a classical stochastic epidemiological model. Specifically, we use the susceptible-infected-susceptible model, which accounts for density-dependent transmission rates and finite total population size, leading to a stochastically changing infected population size. We first validate our method by estimating epidemic parameters for simulated data and then apply it to transmission clusters from the Swiss HIV epidemic. Our estimates of the basic reproductive number R0 for the considered Swiss HIV transmission clusters are significantly higher than previous estimates, which were derived assuming infinite population size. This difference in key parameter estimates highlights the importance of careful model choice when doing phylogenetic inference. In summary, this article presents the first fully stochastic implementation of a classical epidemiological model for phylogenetic inference and thereby addresses a key aspect in ongoing efforts to merge phylogenetics and epidemiology.