Accounting for contact tracing in epidemiological birth-death models.

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 contact tracing schemes are included in health policies of many countries. We extended phylodynamic multi-type birth-death (MTBD) models with contact tracing (CT), and developed a simulator to generate trees under MTBD and MTBD-CT models. We proposed a non-parametric test for detecting contact tracing 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-CT family, the BD-CT(1) model, where only the last contact can be notified, we solved the differential equations and proposed a closed form solution for the likelihood function. We implemented a maximum-likelihood program, which estimates the BD-CT(1) model parameters and their confidence intervals from phylogenetic trees. It performed accurate parameter inference on BD and BD-CT(1) simulated data, and detected contact tracing in HIV-1 B epidemics in Zurich and the UK. Importantly, we showed that not accounting for contact tracing when it is present, leads to bias in parameter estimation with the BD model (overestimation of the becoming-non-infectious rate). This bias is also present, but greatly reduced, when the BD-CT(1) model is used on data where multiple contacts can be notified. Our CT test, MTBD-CT tree simulator and BD-CT(1) parameter estimator are freely available at GitHub (evolbioinfo/treesimulator and evolbioinfo/bdct).