Bayesian phylodynamic inference with complex models

Abstract

Population genetic modeling can enhance Bayesian phylogenetic inference by providing a realistic prior on the distribution of branch lengths and times of common ancestry. The parameters of a population genetic model may also have intrinsic importance, and simultaneous estimation of a phylogeny and model parameters has enabled phylodynamic inference of population growth rates, reproduction numbers, and effective population size through time. Phylodynamic inference based on pathogen genetic sequence data has emerged as useful supplement to epidemic surveillance, however commonly-used mechanistic models that are typically fitted to non-genetic surveillance data are rarely fitted to pathogen genetic data due to a dearth of software tools, and the theory required to conduct such inference has been developed only recently. We present a framework for coalescent-based phylogenetic and phylodynamic inference which enables highly-flexible modeling of demographic and epidemiological processes. This approach builds upon previous structured coalescent approaches and includes enhancements for computational speed, accuracy, and stability. A flexible markup language is described for translating parametric demographic or epidemiological models into a structured coalescent model enabling simultaneous estimation of demographic or epidemiological parameters and time-scaled phylogenies. We demonstrate the utility of these approaches by fitting compartmental epidemiological models to Ebola virus and Influenza A virus sequence data, demonstrating how important features of these epidemics, such as the reproduction number and epidemic curves, can be gleaned from genetic data. These approaches are provided as an open-source package PhyDyn for the BEAST2 phylogenetics platform.

Fig 1. Compartmental diagram representing structure of models for seasonal human Influenza (A) and Ebola virus model (B).

Solid lines represent flux of hosts between different categories. Dash lines represent migration. Dotted lines represent births (transmission).

Fig 2. The estimated effective number of H3N2 human influenza infections in 2004-2005 in New York State.

A. Estimates obtained using the parametric seasonal influenza model described in the text. B. Effective population size estimated using a conventional Bayesian skyline analysis.

Fig 3. Model-based estimates of cumulative infections through time for the 2014-15 Ebola epidemic in Western Africa.

Estimates are shown for the SEIR model (A) and the model which includes super-spreading (B). The red line show the cumulative number of cases reported by WHO [35].

Fig 4. Estimated effective number of infections through time using the superspreading SEIR model for the 2014-15 Ebola epidemic in Western Africa.

The red vertical line shows the time of peak prevalence inferred from WHO case reports. The vertical dashed line shows the model estimated time of peak prevalence. The red trajectory shows the proportion of infections in the high-transmission-rate compartment.

Fig 5. Parameter estimates and credible intervals for 25 simulations with variable transmission risk ratos.

The red points show true parameter value. The parameter β is the per-capita transmission rate, and w₀ and w_h are respectively the transmission risk ratios in the first stage of infection and the high risk group (cf. Eq 12). A-C: Results generated using the QL model. D-F: Results generated using the PL2 model. There is one outlier simulation where the transmission rate parameter could not be estimated precisely and upper bound of the CI was > 70% using both methods.