1Exponential growth is a mathematically convenient model for the early stages of an 2 outbreak of an infectious disease. However, for many pathogens (such as Ebola virus) 3 the initial rate of transmission may be sub-exponential, even before transmission is 4 affected by depletion of susceptible individuals. 5 We present a stochastic multi-scale model capable of representing sub-exponential 6 transmission: an in-homogeneous branching process extending the generalised growth 7 model. To validate the model, we fit it to data from the Ebola epidemic in West Africa 8 (2014)(2015)(2016). We demonstrate how a branching process can be fit to both time series 9 of confirmed cases and chains of infection derived from contact tracing. Our estimates 10 of the parameters suggest transmission of Ebola virus was sub-exponential during this 11 epidemic. Both the time series data and the chains of infections lead to consistent 12 parameter estimates. Differences in the data sets meant consistent estimates were not a 13 foregone conclusion. Finally, we use a simulation study to investigate the properties of 14 our methodology. In particular, we examine the extent to which the estimates obtained 15 from time series data and those obtained from chains of infection data agree.
16Our method, based on a simple branching process, is well suited to real-time analy-17 sis of data collected during contact tracing. Identifying the characteristic early growth 18 dynamics (exponential or sub-exponential), including an estimate of uncertainty, dur-19 ing the first phase of an epidemic should prove a useful tool for preliminary outbreak 20 investigations. 21 2 Alexander E. Zarebski et al Author Summary 22Epidemic forecasts have the potential to support public health decision making in out-23 break scenarios for diseases such as Ebola and influenza. In particular, reliable pre-24 dictions of future incidence data may guide surveillance and intervention responses.
25Existing methods for producing forecasts, based upon mechanistic transmission models, 26 often make an implicit assumption that growth is exponential, at least while susceptible 27 depletion remains negligible. However, empirical studies suggest that many infectious 28 disease outbreaks display sub-exponential growth early in the epidemic. Here we in-29 troduce a mechanistic model of early epidemic growth that allows for sub-exponential 30 growth in incidence. We demonstrate how the model can be applied to the types of data 31 that are typically available in (near) real-time, including time series data on incidence as 32 well as individual-level case series and chains of transmission data. We apply our meth-33 ods to publically available data from the 2014-2016 West Africa Ebola epidemic and 34 demonstrate that early epidemic growth was sub-exponential. We also investigate the 35 statistical properties of our model through a simulation re-estimation study to identify 36 it performance characteristics and avenues for further methodological research. 37 statistics 39 42 intervention...