Basic Reproductive Number for Pandemic Influenza

This paper focuses on a fundamental input parameter for most existing mathematical models of pandemic influenza, the ‘basic reproductive number R0,’ 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 R0 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 R0 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 R0 is useful, it is best viewed as an output of a modeling analysis, not an input. But with R0 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 R0 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 R0 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 R0 based on early exponential growth of reported cases may be significantly upwardly biased.