Inferring epidemiological dynamics with Bayesian coalescent inference: The merits of deterministic and stochastic models

TL;DR

This paper develops Bayesian coalescent models, both stochastic and deterministic, to infer epidemiological parameters from molecular data, comparing their performance and applying them to real infectious disease datasets.

Contribution

It introduces and evaluates stochastic and deterministic coalescent SIR models within a Bayesian framework for epidemic inference, highlighting their relative strengths and limitations.

Findings

Stochastic models outperform deterministic ones in accuracy for small R0 and S0.

Both models effectively estimate parameters for large R0 and S0.

Limitations observed when R0 is near one or populations are small.

Abstract

Estimation of epidemiological and population parameters from molecular sequence data has become central to the understanding of infectious disease dynamics. Various models have been proposed to infer details of the dynamics that describe epidemic progression. These include inference approaches derived from Kingman's coalescent theory. Here, we use recently described coalescent theory for epidemic dynamics to develop stochastic and deterministic coalescent SIR tree priors. We implement these in a Bayesian phylogenetic inference framework to permit joint estimation of SIR epidemic parameters and the sample genealogy. We assess the performance of the two coalescent models and also juxtapose results obtained with BDSIR, a recently published birth-death-sampling model for epidemic inference. Comparisons are made by analyzing sets of genealogies simulated under precisely known epidemiological parameters. Additionally, we analyze influenza A (H1N1) sequence data sampled in the Canterbury region of New Zealand and HIV-1 sequence data obtained from known UK infection clusters. We show that both coalescent SIR models are effective at estimating epidemiological parameters from data with large fundamental reproductive number $R_0$ and large population size $S_0$. Furthermore, we find that the stochastic variant generally outperforms its deterministic counterpart in terms of error, bias, and highest posterior density coverage, particularly for smaller $R_0$ and $S_0$. However, each of these inference models are shown to have undesirable properties in certain circumstances, especially for epidemic outbreaks with $R_0$ close to one or with small effective susceptible populations.