Abstract
Since the beginning of the COVID-19 pandemic, the reproduction number has become a popular epidemiological metric used to communicate the state of the epidemic. At its most basic, is defined as the average number of secondary infections caused by one primary infected individual. seems convenient, because the epidemic is expanding if and contracting if . The magnitude of indicates by how much transmission needs to be reduced to control the epidemic. Using in a naïve way can cause new problems. The reasons for this are threefold: (1) There is not just one definition of but many, and the precise definition of affects both its estimated value and how it should be interpreted. (2) Even with a particular clearly defined , there may be different statistical methods used to estimate its value, and the choice of method will affect the estimate. (3) The availability and type of data used to estimate vary, and it is not always clear what data should be included in the estimation. In this review, we discuss when is useful, when it may be of use but needs to be interpreted with care, and when it may be an inappropriate indicator of the progress of the epidemic. We also argue that careful definition of , and the data and methods used to estimate it, can make a more useful metric for future management of the epidemic.
Highlights
We discuss when R is useful, when it may be of use but needs to be interpreted with care, and when it may be an inappropriate indicator of the progress of the epidemic
We argue that careful definition of R, and the data and methods used to estimate it, can make R a more useful metric for future management of the epidemic
We focus on the definitions of different types of R, for example, the basic reproduction number or the effective reproduction number that can be considered different quantities and their applicability to different phases of an epidemic
Summary
For the simplest mathematical model of the beginning of an outbreak, it is assumed that because only a small fraction of the population has been infected, all potential contacts are with susceptibles. If the population is heterogeneous or structured, defining a reproduction number needs care, as the number of new cases, an infective is expected to cause will depend on both their infectiousness and how well connected they are.
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