Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 611731, Sichuan, People's Republic of China.
Big Data Research Center, University of Electronic Science and Technology of China, Chengdu 611731, Sichuan, People's Republic of China.
Proc Natl Acad Sci U S A. 2018 Dec 11;115(50):12680-12685. doi: 10.1073/pnas.1811115115. Epub 2018 Nov 21.
The basic reproduction number is one of the conceptual cornerstones of mathematical epidemiology. Its classical definition as the number of secondary cases generated by a typical infected individual in a fully susceptible population finds a clear analytical expression in homogeneous and stratified mixing models. Along with the generation time (the interval between primary and secondary cases), the reproduction number allows for the characterization of the dynamics of an epidemic. A clear-cut theoretical picture, however, is hardly found in real data. Here, we infer from highly detailed sociodemographic data two multiplex contact networks representative of a subset of the Italian and Dutch populations. We then simulate an infection transmission process on these networks accounting for the natural history of influenza and calibrated on empirical epidemiological data. We explicitly measure the reproduction number and generation time, recording all individual-level transmission events. We find that the classical concept of the basic reproduction number is untenable in realistic populations, and it does not provide any conceptual understanding of the epidemic evolution. This departure from the classical theoretical picture is not due to behavioral changes and other exogenous epidemiological determinants. Rather, it can be simply explained by the (clustered) contact structure of the population. Finally, we provide evidence that methodologies aimed at estimating the instantaneous reproduction number can operationally be used to characterize the correct epidemic dynamics from incidence data.
基本繁殖数是数学流行病学的概念基石之一。其经典定义为在完全易感人群中，典型感染者产生的次生病例数，在均匀和分层混合模型中可以找到明确的解析表达式。与代际时间（初次病例和次生病例之间的间隔）一起，繁殖数可以用来描述传染病的动态。然而，在实际数据中几乎找不到明确的理论图像。在这里，我们根据高度详细的社会人口统计学数据推断出两个代表意大利和荷兰人群子集的多重接触网络。然后，我们在这些网络上模拟感染传播过程，考虑流感的自然史，并根据经验流行病学数据进行校准。我们明确测量繁殖数和代际时间，并记录所有个体级别的传播事件。我们发现，在现实人群中，基本繁殖数的经典概念是站不住脚的，它不能为传染病的演变提供任何概念性的理解。这种与经典理论图像的背离并不是由于行为变化和其他外生流行病学决定因素造成的。相反，它可以简单地解释为人群的（聚类）接触结构。最后，我们提供了证据，表明旨在估计瞬时繁殖数的方法可以从发病数据中操作地用于描述正确的传染病动态。
