There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-2015 Ebola epidemic in West Africa.

中文翻译：

---

表征早期流行病增长的数学模型：综述。


使用数学模型来深入了解传染病的传播动态并评估不同干预策略的潜在影响有着悠久的传统。数学模型越来越多地用于流行病预测，凸显了设计可靠模型来捕获特定病原体和社会背景的基线传播特征的重要性。然而，我们还需要更完善的模型，特别是要考虑到实际流行病早期增长动态的变化，并更好地理解其中的机制。在这里，我们回顾了从传染病爆发数据中建模和表征早期流行病增长模式的最新进展，并调查了对于捕获各种早期流行病增长曲线（从次指数到指数增长动态）最有用的数学公式类型。具体来说，我们回顾了包含空间细节或现实群体混合结构的数学模型，包括元群体模型、基于个体的网络模型和包含反应行为变化或不均匀混合影响的简单 SIR 型模型。在此过程中，我们还分析了先前设计和校准的基于详细大规模代理模型的模拟数据，以研究现实的社交网络和疾病传播特征如何塑造早期流行病增长模式、一般传播动态以及国际疾病紧急情况的控制，例如如2009年甲型H1N1流感大流行和2014-2015年西非埃博拉疫情。