title: Inferring epidemiological dynamics with Bayesian coalescent inference: the merits of deterministic and stochastic models.
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 susceptible-infected-removed (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 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 United Kingdom infection clusters. We show that both coalescent SIR models are effective at estimating epidemiological parameters from data with large fundamental reproductive number [Formula: see text] and large population size [Formula: see text]. 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 [Formula: see text] and [Formula: see text]. However, each of these inference models is shown to have undesirable properties in certain circumstances, especially for epidemic outbreaks with [Formula: see text] close to one or with small effective susceptible populations.
authors.affiliation: Department of Computer Science, University of Auckland, Auckland, New Zealand 1010 Allan Wilson Centre for Molecular Ecology and Evolution, Palmerston North, New Zealand 4442.
authors.forename: Alex
authors.initials: A
authors.lastname: Popinga
authors.affiliation: Department of Computer Science, University of Auckland, Auckland, New Zealand 1010 Allan Wilson Centre for Molecular Ecology and Evolution, Palmerston North, New Zealand 4442 Massey University, Palmerston North, New Zealand 4442.
authors.forename: Tim
authors.initials: T
authors.lastname: Vaughan
authors.affiliation: Department of Biosystems Science and Engineering, ETH Zürich, Basel, Switzerland 44085 SIB Swiss Institute of Bioinformatics, Lausanne, Switzerland 1015.
authors.forename: Tanja
authors.initials: T
authors.lastname: Stadler
authors.affiliation: Department of Computer Science, University of Auckland, Auckland, New Zealand 1010 Allan Wilson Centre for Molecular Ecology and Evolution, Palmerston North, New Zealand 4442 alexei@cs.auckland.ac.nz.
authors.forename: Alexei J
authors.identifier: http://orcid.org/0000-0003-4454-2576
authors.initials: AJ
authors.lastname: Drummond
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D003198:Computer Simulation; D015658:HIV Infections / Q000453:epidemiology; D015497:HIV-1 / Q000145:classification / Q000235:genetics; D006801:Humans; D053118:Influenza A Virus, H1N1 Subtype / Q000145:classification / Q000235:genetics; D007251:Influenza, Human / Q000453:epidemiology; D008390:Markov Chains; D008962:Models, Theoretical; D017720:Molecular Epidemiology / Q000379:methods; D009010:Monte Carlo Method; D010802:Phylogeny; D011156:Population Density; D011159:Population Surveillance / Q000379:methods; D015203:Reproducibility of Results
keywords: Bayesian inference; coalescent; epidemic; phylodynamics; stochastic