Phylogenetic analysis accounting for age-dependent death and sampling with applications to epidemics

TL;DR

This paper introduces a novel epidemiological model for phylogenetic analysis that accounts for age-dependent recovery and sampling rates, enabling more accurate inference of epidemic dynamics from genetic data.

Contribution

It develops an analytical framework for phylogenetic inference under non-Markovian epidemic models with arbitrary recovery and sampling time distributions.

Findings

Derived likelihood expression for phylogenetic trees under the new model

Facilitates efficient simulation of phylogenies with age-dependent rates

Applied framework to influenza and HIV phylogenies

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. Here we introduce an epidemiological model where infectives leave the epidemic, either by 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, namely an application to influenza and an application to HIV. 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.