  Phylodynamics is a set of population genetics tools that aim at
reconstructing demographic history of a population based on molecular sequences
of individuals sampled from the population of interest. One important task in
phylodynamics is to estimate changes in (effective) population size. When
applied to infectious disease sequences such estimation of population size
trajectories can provide information about changes in the number of infections.
To model changes in the number of infected individuals, current phylodynamic
methods use non-parametric approaches, parametric approaches, and stochastic
modeling in conjunction with likelihood-free Bayesian methods. The first class
of methods yields results that are hard-to-interpret epidemiologically. The
second class of methods provides estimates of important epidemiological
parameters, such as infection and removal/recovery rates, but ignores variation
in the dynamics of infectious disease spread. The third class of methods is the
most advantageous statistically, but relies on computationally intensive
particle filtering techniques that limits its applications. We propose a
Bayesian model that combines phylodynamic inference and stochastic epidemic
models, and achieves computational tractability by using a linear noise
approximation (LNA) --- a technique that allows us to approximate probability
densities of stochastic epidemic model trajectories. LNA opens the door for
using modern Markov chain Monte Carlo tools to approximate the joint posterior
distribution of the disease transmission parameters and of high dimensional
vectors describing unobserved changes in the stochastic epidemic model
compartment sizes (e.g., numbers of infectious and susceptible individuals). We
apply our estimation technique to Ebola genealogies estimated using viral
genetic data from the 2014 epidemic in Sierra Leone and Liberia.
