title: Phylodynamic inference for structured epidemiological models.
abstract: Coalescent theory is routinely used to estimate past population dynamics and demographic parameters from genealogies. While early work in coalescent theory only considered simple demographic models, advances in theory have allowed for increasingly complex demographic scenarios to be considered. The success of this approach has lead to coalescent-based inference methods being applied to populations with rapidly changing population dynamics, including pathogens like RNA viruses. However, fitting epidemiological models to genealogies via coalescent models remains a challenging task, because pathogen populations often exhibit complex, nonlinear dynamics and are structured by multiple factors. Moreover, it often becomes necessary to consider stochastic variation in population dynamics when fitting such complex models to real data. Using recently developed structured coalescent models that accommodate complex population dynamics and population structure, we develop a statistical framework for fitting stochastic epidemiological models to genealogies. By combining particle filtering methods with Bayesian Markov chain Monte Carlo methods, we are able to fit a wide class of stochastic, nonlinear epidemiological models with different forms of population structure to genealogies. We demonstrate our framework using two structured epidemiological models: a model with disease progression between multiple stages of infection and a two-population model reflecting spatial structure. We apply the multi-stage model to HIV genealogies and show that the proposed method can be used to estimate the stage-specific transmission rates and prevalence of HIV. Finally, using the two-population model we explore how much information about population structure is contained in genealogies and what sample sizes are necessary to reliably infer parameters like migration rates.
authors.affiliation: Biology Department, Duke University, Durham, North Carolina, United States of America.
authors.forename: David A
authors.initials: DA
authors.lastname: Rasmussen
authors.affiliation: Department of Infectious Disease Epidemiology, Imperial College London, London, United Kingdom.
authors.forename: Erik M
authors.initials: EM
authors.lastname: Volz
authors.affiliation: Biology Department, Duke University, Durham, North Carolina, United States of America; Fogarty International Center, National Institutes of Health, Bethesda, Maryland, United States of America.
authors.forename: Katia
authors.initials: K
authors.lastname: Koelle
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D016021:Epidemiologic Studies; D016013:Likelihood Functions; D008390:Markov Chains; D015233:Models, Statistical; D009010:Monte Carlo Method; D010802:Phylogeny; D013269:Stochastic Processes
references.citation: Philos Trans R Soc Lond B Biol Sci. 2010 Jun 27;365(1548):1879-90
references.pmid: 20478883
references.citation: Annu Rev Phys Chem. 2007;58:35-55
references.pmid: 17037977
references.citation: PLoS Med. 2013 Dec;10(12):e1001568; discussion e1001568
references.pmid: 24339751
references.citation: Theor Popul Biol. 1990 Dec;38(3):331-50
references.pmid: 2293402
references.citation: PLoS Comput Biol. 2011 Aug;7(8):e1002136
references.pmid: 21901082
references.citation: Genetics. 1998 May;149(1):429-34
references.pmid: 9584114
references.citation: Science. 2004 Jan 16;303(5656):327-32
references.pmid: 14726583
references.citation: J R Soc Interface. 2012 May 7;9(70):997-1007
references.pmid: 21920961
references.citation: Philos Trans R Soc Lond B Biol Sci. 2013 Feb 04;368(1614):20120314
references.pmid: 23382432
references.citation: Syst Biol. 1998 Mar;47(1):125-33
references.pmid: 12064232
references.citation: Genetics. 2009 Dec;183(4):1421-30
references.pmid: 19797047
references.citation: PLoS Med. 2012;9(7):e1001232
references.pmid: 22802728
references.citation: PLoS Comput Biol. 2009 Sep;5(9):e1000520
references.pmid: 19779555
references.citation: Proc Natl Acad Sci U S A. 2012 Sep 11;109(37):15066-71
references.pmid: 22927414
references.citation: Lancet. 2011 Jul 16;378(9787):256-68
references.pmid: 21684591
references.citation: Genetics. 1999 Jun;152(2):763-73
references.pmid: 10353916
references.citation: Proc Natl Acad Sci U S A. 2001 Apr 10;98(8):4563-8
references.pmid: 11287657
references.citation: PLoS Comput Biol. 2012;8(6):e1002552
references.pmid: 22761556
references.citation: Proc Natl Acad Sci U S A. 2013 Sep 24;110(39):15538-43
references.pmid: 24009342
references.citation: Genetics. 2013 Nov;195(3):1055-62
references.pmid: 24037268
references.citation: Annu Rev Genet. 1995;29:401-21
references.pmid: 8825481
references.citation: BMC Evol Biol. 2007 Nov 08;7:214
references.pmid: 17996036
references.citation: PLoS Med. 2006 Jul;3(7):e262
references.pmid: 16822094
references.citation: Lancet. 2009 Jan 3;373(9657):48-57
references.pmid: 19038438
references.citation: J Infect Dis. 2008 Sep 1;198(5):687-93
references.pmid: 18662132
references.citation: Genetics. 2000 Jul;155(3):1429-37
references.pmid: 10880500
references.citation: Mol Biol Evol. 2012 Jan;29(1):347-57
references.pmid: 21890480
references.citation: J Infect Dis. 2004 May 15;189(10):1785-92
references.pmid: 15122514
references.citation: Mol Biol Evol. 2014 Feb;31(2):258-71
references.pmid: 24150038
references.citation: Mol Biol Evol. 2005 May;22(5):1185-92
references.pmid: 15703244
references.citation: Genetics. 2012 Jan;190(1):187-201
references.pmid: 22042576
references.citation: J Math Biol. 1990;29(1):59-75
references.pmid: 2277236
references.citation: J Infect Dis. 2011 Nov;204(9):1463-9
references.pmid: 21921202
references.citation: Philos Trans R Soc Lond B Biol Sci. 1995 Jul 29;349(1327):25-31
references.pmid: 8748016
references.citation: PLoS Med. 2008 Mar 18;5(3):e50
references.pmid: 18351795
references.citation: Mol Biol Evol. 2001 Dec;18(12):2298-305
references.pmid: 11719579
references.citation: Bioinformatics. 2006 Mar 15;22(6):768-70
references.pmid: 16410317