Bayesian Coalescent Epidemic Inference: Comparison of Stochastic and Deterministic SIR Population Dynamics

Bayesian Coalescent Epidemic Inference: Comparison of Stochastic and Deterministic SIR Population Dynamics

Alex Popinga, Tim Vaughan, Tanja Stadler, Alexei Drummond
Comments: Submitted
Subjects: Populations and Evolution (q-bio.PE)

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 Kingmans coalescent as well as from birth death branching processes. The development of alternative approaches merits investigation of their characteristics and differences. 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 models performance and contrast results obtained with a recently published birth death sampling model for epidemic inference. Comparisons are made by analyzing sets of genealogies simulated under precisely known epidemiological parameters. We also compare results of analyses using published HIV1 sequence data obtained from known UK infection clusters. We show that the coalescent SIR model is effective at estimating epidemiological parameters from data with large fundamental reproductive number R0 and large population size S0. We find that the stochastic variant generally outperforms its deterministic counterpart. However, each of these Bayesian estimators are shown to have undesirable properties in certain circumstances, especially for epidemic outbreaks with R0 close to one or with small susceptible populations.

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