Inference for Nonlinear Epidemiological Models Using Genealogies and Time Series

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Abstract
Phylodynamics - the field aiming to quantitatively integrate the ecological and evolutionary dynamics of rapidly evolving populations like those of RNA viruses – increasingly relies upon coalescent approaches to infer past population dynamics from reconstructed genealogies. As sequence data have become more abundant, these approaches are beginning to be used on populations undergoing rapid and rather complex dynamics. In such cases, the simple demographic models that current phylodynamic methods employ can be limiting. First, these models are not ideal for yielding biological insight into the processes that drive the dynamics of the populations of interest. Second, these models differ in form from mechanistic and often stochastic population dynamic models that are currently widely used when fitting models to time series data. As such, their use does not allow for both genealogical data and time series data to be considered in tandem when conducting inference. Here, we present a flexible statistical framework for phylodynamic inference that goes beyond these current limitations. The framework we present employs a recently developed method known as particle MCMC to fit stochastic, nonlinear mechanistic models for complex population dynamics to gene genealogies and time series data in a Bayesian framework. We demonstrate our approach using a nonlinear Susceptible-Infected-Recovered (SIR) model for the transmission dynamics of an infectious disease and show through simulations that it provides accurate estimates of past disease dynamics and key epidemiological parameters from genealogies with or without accompanying time series data. Reliable information about the demographic history of populations is important to both population biologists and epidemiologists, but is often absent or unreliable. There has therefore been great interest in developing statistical methods for inferring past population dynamics from gene genealogies reconstructed from molecular sequences. These “phylodynamic” methods take advantage of the fact that changes in population size can dramatically affect the shape of genealogies, making it possible to infer past changes in population size from a genealogy. However, in order for past population dynamics to be inferred, a demographic model must be specified. Current methods use demographic models that are often too simple for populations undergoing complex dynamics and generally do not allow for the parameters influencing the population dynamics to be estimated. We show how current phylodynamic methods can be extended to allow a much wider class of models to be fit to genealogies and illustrate our approach using an epidemiological model for the transmission of an infectious disease.