Chowell Gerardo, Viboud Cécile, Simonsen Lone, Moghadas Seyed M
School of Public Health, Georgia State University, Atlanta, GA, USA Division of International Epidemiology and Population Studies, Fogarty International Center, National Institutes of Health, Bethesda, MD, USA
Division of International Epidemiology and Population Studies, Fogarty International Center, National Institutes of Health, Bethesda, MD, USA.
J R Soc Interface. 2016 Oct;13(123). doi: 10.1098/rsif.2016.0659.
Early estimates of the transmission potential of emerging and re-emerging infections are increasingly used to inform public health authorities on the level of risk posed by outbreaks. Existing methods to estimate the reproduction number generally assume exponential growth in case incidence in the first few disease generations, before susceptible depletion sets in. In reality, outbreaks can display subexponential (i.e. polynomial) growth in the first few disease generations, owing to clustering in contact patterns, spatial effects, inhomogeneous mixing, reactive behaviour changes or other mechanisms. Here, we introduce the generalized growth model to characterize the early growth profile of outbreaks and estimate the effective reproduction number, with no need for explicit assumptions about the shape of epidemic growth. We demonstrate this phenomenological approach using analytical results and simulations from mechanistic models, and provide validation against a range of empirical disease datasets. Our results suggest that subexponential growth in the early phase of an epidemic is the rule rather the exception. Mechanistic simulations show that slight modifications to the classical susceptible-infectious-removed model result in subexponential growth, and in turn a rapid decline in the reproduction number within three to five disease generations. For empirical outbreaks, the generalized-growth model consistently outperforms the exponential model for a variety of directly and indirectly transmitted diseases datasets (pandemic influenza, measles, smallpox, bubonic plague, cholera, foot-and-mouth disease, HIV/AIDS and Ebola) with model estimates supporting subexponential growth dynamics. The rapid decline in effective reproduction number predicted by analytical results and observed in real and synthetic datasets within three to five disease generations contrasts with the expectation of invariant reproduction number in epidemics obeying exponential growth. The generalized-growth concept also provides us a compelling argument for the unexpected extinction of certain emerging disease outbreaks during the early ascending phase. Overall, our approach promotes a more reliable and data-driven characterization of the early epidemic phase, which is important for accurate estimation of the reproduction number and prediction of disease impact.
新兴和再发感染传播潜力的早期估计越来越多地用于向公共卫生当局通报疫情所构成的风险水平。现有的估计繁殖数的方法通常假定在易感人群耗尽之前，病例发病率在疾病的最初几代呈指数增长。实际上，由于接触模式的聚集、空间效应、不均匀混合、反应性行为变化或其他机制，疫情在最初几代可能呈现亚指数（即多项式）增长。在此，我们引入广义增长模型来描述疫情的早期增长特征并估计有效繁殖数，而无需对疫情增长的形状做出明确假设。我们使用机理模型的分析结果和模拟来证明这种现象学方法，并针对一系列经验性疾病数据集进行验证。我们的结果表明，疫情早期的亚指数增长是常态而非例外。机理模拟表明，对经典的易感-感染-康复模型进行轻微修改会导致亚指数增长，进而使繁殖数在三到五代疾病内迅速下降。对于经验性疫情，广义增长模型在各种直接和间接传播疾病的数据集（大流行性流感、麻疹、天花、腺鼠疫、霍乱、口蹄疫、艾滋病毒/艾滋病和埃博拉）中始终优于指数模型，模型估计支持亚指数增长动态。分析结果预测并在真实和合成数据集中观察到的有效繁殖数在三到五代疾病内迅速下降，这与遵循指数增长的疫情中繁殖数不变的预期形成对比。广义增长概念还为某些新兴疾病疫情在早期上升阶段意外消亡提供了一个有说服力的论据。总体而言，我们的方法促进了对疫情早期阶段更可靠且基于数据的特征描述，这对于准确估计繁殖数和预测疾病影响非常重要。
