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Estimation of epidemiological and population parameters from molecularsequence data has become central to the understanding of infectious diseasedynamics. Various models have been proposed to infer details of the dynamicsthat describe epidemic progression. These include inference approaches derivedfrom Kingman's coalescent theory. Here, we use recently described coalescenttheory for epidemic dynamics to develop stochastic and deterministic coalescentSIR tree priors. We implement these in a Bayesian phylogenetic inferenceframework to permit joint estimation of SIR epidemic parameters and the samplegenealogy. We assess the performance of the two coalescent models and alsojuxtapose results obtained with BDSIR, a recently publishedbirth-death-sampling model for epidemic inference. Comparisons are made byanalyzing sets of genealogies simulated under precisely known epidemiologicalparameters. Additionally, we analyze influenza A (H1N1) sequence data sampledin the Canterbury region of New Zealand and HIV-1 sequence data obtained fromknown UK infection clusters. We show that both coalescent SIR models areeffective at estimating epidemiological parameters from data with largefundamental reproductive number $R_0$ and large population size $S_0$.Furthermore, we find that the stochastic variant generally outperforms itsdeterministic counterpart in terms of error, bias, and highest posteriordensity coverage, particularly for smaller $R_0$ and $S_0$. However, each ofthese inference models are shown to have undesirable properties in certaincircumstances, especially for epidemic outbreaks with $R_0$ close to one orwith small effective susceptible populations.

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