Phylodynamic Inference for Structured Epidemiological Models

Coalescent theory is routinely used to estimate past population dynamics and demographic parameters from genealogies. While early work in coalescent theory only considered simple demographic models, advances in theory have allowed for increasingly complex demographic scenarios to be considered. The success of this approach has lead to coalescent-based inference methods being applied to populations with rapidly changing population dynamics, including pathogens like RNA viruses. However, fitting epidemiological models to genealogies via coalescent models remains a challenging task, because pathogen populations often exhibit complex, nonlinear dynamics and are structured by multiple factors. Moreover, it often becomes necessary to consider stochastic variation in population dynamics when fitting such complex models to real data. Using recently developed structured coalescent models that accommodate complex population dynamics and population structure, we develop a statistical framework for fitting stochastic epidemiological models to genealogies. By combining particle filtering methods with Bayesian Markov chain Monte Carlo methods, we are able to fit a wide class of stochastic, nonlinear epidemiological models with different forms of population structure to genealogies. We demonstrate our framework using two structured epidemiological models: a model with disease progression between multiple stages of infection and a two-population model reflecting spatial structure. We apply the multi-stage model to HIV genealogies and show that the proposed method can be used to estimate the stage-specific transmission rates and prevalence of HIV. Finally, using the two-population model we explore how much information about population structure is contained in genealogies and what sample sizes are necessary to reliably infer parameters like migration rates.Author Summary: Mathematical models play an important role in our understanding of what processes drive the complex population dynamics of infectious pathogens. Yet developing statistical methods for fitting models to epidemiological data is difficult. Epidemiological data is often noisy, incomplete, aggregated across different scales and generally provides only a partial picture of the underlying disease dynamics. Using nontraditional sources of data, like molecular sequences of pathogens, can provide additional information about epidemiological dynamics. But current “phylodynamic” inference methods for fitting models to genealogies reconstructed from sequence data have a number of major limitations. We present a statistical framework that builds upon earlier work to address two of these limitations: population structure and stochasticity. By incorporating population structure, our framework can be applied in cases where the host population is divided into different subpopulations, such as by spatial isolation. Our framework also takes into consideration stochastic noise and can therefore capture the inherent variability of epidemiological dynamics. These advances allow for a much wider class of epidemiological models to be fit to genealogies in order to estimate key epidemiological parameters and to reconstruct past disease dynamics.