Department of Mathematics, Pennsylvania State University, University Park, State College, PA 16802, USA.
Comput Math Methods Med. 2011;2011:527610. doi: 10.1155/2011/527610. Epub 2011 Aug 16.
The basic reproductive ratio, R(0), is one of the fundamental concepts in mathematical biology. It is a threshold parameter, intended to quantify the spread of disease by estimating the average number of secondary infections in a wholly susceptible population, giving an indication of the invasion strength of an epidemic: if R(0) < 1, the disease dies out, whereas if R(0) > 1, the disease persists. R(0) has been widely used as a measure of disease strength to estimate the effectiveness of control measures and to form the backbone of disease-management policy. However, in almost every aspect that matters, R(0) is flawed. Diseases can persist with R(0) < 1, while diseases with R(0) > 1 can die out. We show that the same model of malaria gives many different values of R(0), depending on the method used, with the sole common property that they have a threshold at 1. We also survey estimated values of R(0) for a variety of diseases, and examine some of the alternatives that have been proposed. If R(0) is to be used, it must be accompanied by caveats about the method of calculation, underlying model assumptions and evidence that it is actually a threshold. Otherwise, the concept is meaningless.
基本繁殖数 R(0) 是数学生物学中的基本概念之一。它是一个阈值参数，旨在通过估计易感人群中的平均二次感染数来量化疾病的传播，从而表明传染病的入侵强度：如果 R(0) < 1，则疾病会消失，而如果 R(0) > 1，则疾病会持续存在。R(0) 已被广泛用作衡量疾病强度的指标，用于估计控制措施的有效性，并为疾病管理政策提供基础。然而，在几乎所有重要方面，R(0) 都存在缺陷。疾病可以在 R(0) < 1 的情况下持续存在，而 R(0) > 1 的疾病也可能消失。我们表明，疟疾的相同模型会根据使用的方法给出许多不同的 R(0) 值，唯一的共同点是它们在 1 处有一个阈值。我们还调查了各种疾病的 R(0) 的估计值，并研究了一些已提出的替代方法。如果要使用 R(0)，则必须说明计算方法、基本模型假设以及它实际上是一个阈值的证据，否则该概念毫无意义。
