Inference for Nonlinear Epidemiological Models Using Genealogies and Time Series

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.

Quantifying the epidemic spread of Ebola virus (EBOV) in Sierra Leone using phylodynamics

“…This study shows that phylodynamics allows estimation of these parameters from sparse collection of single samples per patient in a population, without the need for details of their contacts or duration of symptoms. Combining such methods with classical epidemiological measurements 19 will help improve the precision of these estimates for real-time epidemic studies, providing public health entities with better information on which to base critical control decisions.…”

Bayesian hierarchical statistical SIRS models

“…A wide range of inference techniques have been proposed and implemented in the R statistical language as part of the package pomp (http://cran.at.r-project.org/web/packages/pomp/), such as nonlinear forecasting (e.g., Kendall et al, 1999;Kendall et al, 2005), iterated filtering (Ionides et al, 2006;King et al, 2008;He et al, 2010), and approximate Bayesian particle filtering (e.g., Liu and West, 2001;Arulampalam et al, 2001;Dukić et al, 2012;Rasmussen et al, 2011). Some more recent state-space models involve spatial components in the dynamical process model (e.g., Patterson et al, 2008).…”

“…Some of these models are not appropriate for modeling epidemic flows (e.g., Kendall et al, 1999;Kendall et al, 2005;Patterson et al, 2008). Those that are extensions of classic compartment epidemic models (e.g., the SIR model and the SEIR model) and that do pay attention to the underlying true process hidden behind the noisy data, either ignore the source of variation that captures randomness in the (hidden) epidemic process (e.g., Rasmussen et al, 2011), or they do not preserve the mass-balance property (e.g., Liu and West, 2001;Dukić et al, 2012), which may introduce biased results. Recent extensions to stochastic models with a master equation have similar problems with mass balance (e.g., Alonso et al, 2007).…”

Particle filters and Markov chains for learning of dynamical systems

“…In a population of constant size, we let S t , I t and R t represent the fractions of susceptible, infected and recovered individuals at time t, respectively. Rasmussen et al (2011) study a time-discrete SIR model with environmental noise and seasonal fluctuations, which is given by S t+1 = S t + µ − µS t − β t S t I t v t , (1.2a) I t+1 = I t − (γ + µ)I t + β t S t I t v t , (1.2b) R t+1 = R t + γI t − µR t .…”