A sub-exponential branching process to study early epidemic dynamics with application to Ebola

Exponential growth is a mathematically convenient model for the early stages of an outbreak of an infectious disease. However, for many pathogens (such as Ebola virus) the initial rate of transmission may be sub-exponential, even before transmission is affected by depletion of susceptible individuals.\n\nWe present a stochastic multi-scale model capable of representing sub-exponential transmission: an in-homogeneous branching process extending the generalised growth model. To validate the model, we fit it to data from the Ebola epidemic in West Africa (2014-2016). We demonstrate how a branching process can be fit to both time series of confirmed cases and chains of infection derived from contact tracing. Our estimates of the parameters suggest transmission of Ebola virus was sub-exponential during this epidemic. Both the time series data and the chains of infections lead to consistent parameter estimates. Differences in the data sets meant consistent estimates were not a foregone conclusion. Finally, we use a simulation study to investigate the properties of our methodology. In particular, we examine the extent to which the estimates obtained from time series data and those obtained from chains of infection data agree.\n\nOur method, based on a simple branching process, is well suited to real-time analysis of data collected during contact tracing. Identifying the characteristic early growth dynamics (exponential or sub-exponential), including an estimate of uncertainty, during the first phase of an epidemic should prove a useful tool for preliminary outbreak investigations.\n\nAuthor SummaryEpidemic forecasts have the potential to support public health decision making in outbreak scenarios for diseases such as Ebola and influenza. In particular, reliable predictions of future incidence data may guide surveillance and intervention responses. Existing methods for producing forecasts, based upon mechanistic transmission models, often make an implicit assumption that growth is exponential, at least while susceptible depletion remains negligible. However, empirical studies suggest that many infectious disease outbreaks display sub-exponential growth early in the epidemic. Here we introduce a mechanistic model of early epidemic growth that allows for sub-exponential growth in incidence. We demonstrate how the model can be applied to the types of data that are typically available in (near) real-time, including time series data on incidence as well as individual-level case series and chains of transmission data. We apply our methods to publically available data from the 2014-2016 West Africa Ebola epidemic and demonstrate that early epidemic growth was sub-exponential. We also investigate the statistical properties of our model through a simulation re-estimation study to identify it performance characteristics and avenues for further methodological research.