A computationally tractable birth-death model that combines phylogenetic and epidemiological data

Inferring the dynamics of pathogen transmission during an outbreak is an important problem in infectious disease epidemiology. In mathematical epidemiology, estimates are often informed by time series of confirmed cases, while in phylodynamics genetic sequences of the pathogen, sampled through time, are the primary data source. Each type of data provides different, and potentially complementary, insight. Recent studies have recognised that combining data sources can improve estimates of the transmission rate and the number of infected individuals. However, inference methods are typically highly specialised and field-specific and are either computationally prohibitive or require intensive simulation, limiting their real-time utility. We present a novel birth-death phylogenetic model and derive a tractable analytic approximation of its likelihood, the computational complexity of which is linear in the size of the dataset. This approach combines epidemiological and phylodynamic data to produce estimates of key parameters of transmission dynamics and the unobserved prevalence. Using simulated data, we show (a) that the approximation agrees well with existing methods, (b) validate the claim of linear complexity and (c) explore robustness to model misspecification. This approximation facilitates inference on large datasets, which is increasingly important as large genomic sequence datasets become commonplace.Author summary: Mathematical epidemiologists typically study time series of cases, ie the epidemic curve, to understand the spread of pathogens. Genetic epidemiologists study similar problems but do so using observations of the genetic sequence of the pathogen, which also contains information about the transmission process. There have been many attempts to unite these approaches and utilise both data sources. However, striking a suitable balance between model flexibility and fidelity, in a computationally tractable way, has proven challenging. There are several competing methods, but they are often intractable when applied to a large dataset. As sequencing of pathogen genomes becomes common, and an increasing amount of epidemiological data are collected, this situation will only be exacerbated. To bridge the gap between the time series and genomic methods we developed an approximation scheme, called TimTam. TimTam can accurately and efficiently estimate key features of an epidemic, such as the prevalence of infection (how many people are currently infected) and the basic reproduction number (a measure of the transmissibility of the infection.).