Revisiting R[subscript 0], the Basic Reproductive Number for Pandemic Influenza

Abstract

This paper focuses on a fundamental input parameter for most existing mathematical models of pandemic influenza, the ‘basic reproductive number R[subscript 0],’ defined to be the mean number of new influenza infections created by a newly infected person in a population of all susceptible people. We argue that R[subscript 0] is limited in policy and scientific value as is any single parameter attempting to characterize a complex probabilistic process. In particular, we demonstrate by simple logic that R[subscript 0] does not exist as a separate ‘constant of a particular influenza,’ but rather its value is determined by social context and behavioral patterns as well as by the “physics’’ of the influenza virus. To the extent that R[subscript 0] is useful, it is best viewed as an output of a modeling analysis, not an input. But with R[subscript 0] being the mean of a random variable, much more information is contained in the entire probability distribution. With this view, we show – again by simple arguments – that R[subscript 0] can be greater than 1.0 and still, contrary to popular belief, the probability of an exponentially growing pandemic may be arbitrarily small. Finally, we show that attempts to estimate R[subscript 0] from data of previous pandemics is fraught with methodological complexities, due primarily to heterogeneities in the population that cause super-spreaders and socially active people to be the first propagators of the disease. Unless one is careful, statistical estimates of R[subscript 0] based on early exponential growth of reported cases may be significantly upwardly biased.