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

<jats:p>Inferring the dynamics of pathogen transmission during an outbreak is an important problem in both infectious disease epidemiology and phylodynamics. In mathematical epidemiology, estimates are often informed by time-series of infected cases while in phylodynamics genetic sequences sampled through time are the primary data source. Each data type provides different, and potentially complementary, insights into transmission. However inference methods are typically highly specialised and field-specific. Recent studies have recognised the benefits of combining data sources, which include improved estimates of the transmission rate and number of infected individuals. However, the methods they employ are either computationally prohibitive or require intensive simulation, limiting their real-time utility. We present a novel birth-death phylogenetic model, called TimTam which can be informed by both phylogenetic and epidemiological data. Moreover, we derive a tractable analytic approximation of the TimTam likelihood, the computational complexity of which is linear in the size of the data set. Using the TimTam we show how key parameters of transmission dynamics and the number of unreported infections can be estimated accurately using these heterogeneous data sources. The approximate likelihood facilitates inference on large data sets, an important consideration as such data become increasingly common due to improving sequencing capability.</jats:p>