title: Phylogenetic analysis accounting for age-dependent death and sampling with applications to epidemics.
abstract: The reconstruction of phylogenetic trees based on viral genetic sequence data sequentially sampled from an epidemic provides estimates of the past transmission dynamics, by fitting epidemiological models to these trees. To our knowledge, none of the epidemiological models currently used in phylogenetics can account for recovery rates and sampling rates dependent on the time elapsed since transmission, i.e. age of infection. Here we introduce an epidemiological model where infectives leave the epidemic, by either recovery or sampling, after some random time which may follow an arbitrary distribution. We derive an expression for the likelihood of the phylogenetic tree of sampled infectives under our general epidemiological model. The analytic concept developed in this paper will facilitate inference of past epidemiological dynamics and provide an analytical framework for performing very efficient simulations of phylogenetic trees under our model. The main idea of our analytic study is that the non-Markovian epidemiological model giving rise to phylogenetic trees growing vertically as time goes by can be represented by a Markovian "coalescent point process" growing horizontally by the sequential addition of pairs of coalescence and sampling times. As examples, we discuss two special cases of our general model, described in terms of influenza and HIV epidemics. Though phrased in epidemiological terms, our framework can also be used for instance to fit macroevolutionary models to phylogenies of extant and extinct species, accounting for general species lifetime distributions.
authors.affiliation: Sorbonne Universités, UPMC Univ Paris 06, UMR 7599 Laboratoire de Probabilités et Modèles Aléatoires, France; Collège de France, UMR 7241 Center for Interdisciplinary Research in Biology, F-75005 Paris, France. Electronic address: amaury.lambert@upmc.fr.
authors.forename: Amaury
authors.initials: A
authors.lastname: Lambert
authors.affiliation: Institute of Integrative Biology, ETH Zürich, Universitätsstrasse 16, 8092 Zürich, Switzerland. Electronic address: helen.alexander@env.ethz.ch.
authors.forename: Helen K
authors.initials: HK
authors.lastname: Alexander
authors.affiliation: Institute of Integrative Biology, ETH Zürich, Universitätsstrasse 16, 8092 Zürich, Switzerland. Electronic address: tanja.stadler@env.ethz.ch.
authors.forename: Tanja
authors.initials: T
authors.lastname: Stadler
mesh_terms: D016021:Epidemiologic Studies; D015658:HIV Infections / Q000453:epidemiology; D006801:Humans; D007251:Influenza, Human / Q000453:epidemiology; D016013:Likelihood Functions; D008390:Markov Chains; D008962:Models, Theoretical; D010802:Phylogeny
keywords: Birth–death process; Coalescent point process; Contour process; HIV; Influenza