A generalized-growth model to characterize the early ascending phase of infectious disease outbreaks

Viboud, C'ecile; Simonsen, Lone; Chowell, Gerardo

A better characterization of the early growth dynamics of an epidemic is needed to dissect the important drivers of disease transmission. We introduce a 2-parameter generalized-growth model to characterize the ascending phase of an outbreak and capture epidemic profiles ranging from sub-exponential to exponential growth. We test the model against empirical outbreak data representing a variety of viral pathogens and provide simulations highlighting the importance of sub-exponential growth for forecasting purposes. We applied the generalized-growth model to 20 infectious disease outbreaks representing a range of transmission routes. We uncovered epidemic profiles ranging from very slow growth (p=0.14 for the Ebola outbreak in Bomi, Liberia (2014)) to near exponential (p>0.9 for the smallpox outbreak in Khulna (1972), and the 1918 pandemic influenza in San Francisco). The foot-and-mouth disease outbreak in Uruguay displayed a profile of slower growth while the growth pattern of the HIV/AIDS epidemic in Japan was approximately linear. The West African Ebola epidemic provided a unique opportunity to explore how growth profiles vary by geography; analysis of the largest district-level outbreaks revealed substantial growth variations (mean p=0.59, range: 0.14-0.97). Our findings reveal significant variation in epidemic growth patterns across different infectious disease outbreaks and highlights that sub-exponential growth is a common phenomenon. Sub-exponential growth profiles may result from heterogeneity in contact structures or risk groups, reactive behavior changes, or the early onset of interventions strategies, and consideration of"deceleration parameters"may be useful to refine existing mathematical transmission models and improve disease forecasts.