We present several models for the genealogical structure of pathogens. Our approach is to extend commonly used compartmental models, such as the susceptible-infected-recovered model. This approach is premised on the assumption that each lineage in a genealogy corresponds to a single infected host and each node corresponds to a transmission between hosts. Call this genealogy the 'transmission genealogy'. Under suitable assumptions about the natural history and immunological dynamics of a pathogen, the phylogeny of a pathogen will correspond to the transmission genealogy. We show that this is a valid approximation if super-infection is rare (a host becomes infected once and only once) and if the effective population size of the pathogen within hosts is very small. Under these conditions, we outline a coalescent mathematical model (a model which describes genealogical structure on a retrospective time axis), which relates the genealogical structure predicted by epidemiological models to phylogenies which may be estimated from pathogen genetic sequence data. This theory enables the estimation of compartmental model parameters from pathogen genetic data. We present several applications of this theory. First, we illustrate under what conditions the effective population size of the pathogen at the epidemic level will correspond to the the true prevalence of infection. We show that the correspondence between effective size and prevalence is good during the early exponential growth period of an epidemic, but that the correspondence can be very bad if the per-capita incidence rate changes rapidly through time. Secondly, we fit two simple compartmental SIR models to a phylogeny of S. aureaus, yielding an estimate of R0 and the early epidemic growth rate. Thirdly, we fit a complex compartmental model for the HIV epidemic to a phylogeny estimated from 662 subtype B HIV-1 sequences. By fitting this model, we estimate that 45% of transmissions likely occur during the first year of the infectious period. Finally, we discuss applications of the coalescent models to the problem of inferring the source of infection (transmission pairs) in large random samples of infected hosts and corresponding pathogen sequences.

Host: Thomas Leitner