Accounting for partner notification in epidemiological birth-death-models

Abstract

Phylodynamics bridges the gap between classical epidemiology and pathogen genome sequence data by estimating epidemiological parameters from time-scaled pathogen phylogenetic trees. The models used in phylodynamics typically assume that the sampling procedure is independent between infected individuals. However, this assumption does not hold for many epidemics, in particular for such sexually transmitted infections as HIV-1, for which partner notification schemes are included in health policies of many countries. We developed an extension of phylodynamic multi-type birth-death (MTBD) models with partner notification (PN), and a simulator to generate trees under MTBD and MTBD-PN models. We proposed a non-parametric test for detecting partner notification in pathogen phylogenetic trees. Its application to simulated data showed that it is both highly specific and sensitive. For the simplest representative of the MTBD-PN family, the BD-PN model, we solved the differential equations and proposed a closed form solution for the likelihood function. We implemented it in a program, which estimates the model parameters and their confidence intervals from phylogenetic trees. It performed accurate estimations on simulated data, and detected partner notification in HIV-1 B epidemics in Zurich and the UK. Importantly, we showed that not accounting for partner notification when it is present leads to bias in parameter estimation with the BD model, while BD-PN parameter estimator performs well both in presence and in absence of partner notification. Our PN test, MTBD-PN tree simulator and BD-PN parameter estimator are freely available at https://github.com/evolbioinfo/treesimulator and https://github.com/evolbioinfo/bdpn}{github.com/evolbioinfo/bdpn.