We begin with a discussion of plausible transmissibility of a newly emerged influenza strain, in terms of the basic reproduction number.
Estimates of the basic reproduction number for common SEIR infectious diseases range from 4-7 for diphtheria and poliomyelitis to 14-18 for measles and pertussis; see Anderson and May (1991). In contrast, guided by data on attack rates and excess mortality reported for past pandemics of influenza, recent work on modeling the possible control of a newly emerged strain of influenza in South East Asian [Longini et al. (2005), Ferguson et al. (2005)] has focused a great deal on values of R0 in the range of 1.5 to 2.5. Is this a plausible range for R0?
It is of course possible that the next pandemic strain of influenza will be completely different and will have a very large value of R0, and we must not ignore such a possible scenario. However, it seems appropriate to focus planning mainly on a range of values judged to be plausible on the basis of past experience. We have focused mainly on the range of values from 1.5 to 3.5, and support this choice with the following observations:
i. The first question we might ask is: Given that most circulating infectious diseases are estimated to have a larger R0, how can a currently circulating influenza virus with R0 in the range 1.5-3.5 possibly avoid eradication?
Three characteristics of influenza help to make this possible. Firstly, it is evident that individuals infected with influenza are infectious before they show symptoms [Fraser et al. (2004), Day et al. (2006), WHO Writing Group (2006)]. As a result, some infection occurs before the source case is symptomatic. Secondly, the virus (especially the influenza A virus) has the ability to change with the result that immunity wanes [Fox et al. (1982)], leaving individuals susceptible to re-infection (in contrast to infections such as measles and chickenpox that confer lasting immunity). Thirdly, the same drift in the virus means that influenza vaccines tend to have an efficacy that is low relative to that of the measles vaccine, for example King et al. (1991) and Turner et al. (2003).
ii. Data on infections within households, where contacts are considered to be more frequent and ‘closer’, are not consistent with a large value of R0. For example, in a study of households from Tecumseh, Michigan [Monto et al. (1985)] sera from all members in a large number of households were tested before and after the influenza epidemic season to see who was susceptible at the beginning and who was infected by the end of the study period. An attractive feature of this study is that asymptomatic infection should be detected by this approach. The observation that among households with at least one primary case the influenza attack rate among the remaining household members was only 24% is not consistent with a large value of R0.
iii. The reported clinical influenza attack rates in pandemics of the last century are mainly between 25% and 35% [Nguyen-Van-Tam and Hampson (2003)]. There may have been a substantial number of influenza infections that did not meet the case definition used, though a value of R0 greater than 3.5 is not suggested even if we double the reported clinical attack rates. Admittedly, the 1918 pandemic achieved its moderate attack rate only with substantial efforts aimed at social distancing and without this the attack rate would undoubtedly have been higher.
iv. There are settings in which a much higher influenza attack rate has been observed, specifically in influenza-na´ve populations in Alaska [Crosby (1976)] and Tristan da Cunha [Mantle and Tyrrell (1973)]. This suggests that the basic reproduction number, corresponding to a completely na´ve population, can be much larger and that most populations exposed to pandemic influenza had the good fortune of partial immunity to the newly emerged strain of the virus, presumably as a result of past exposure to circulating influenza viruses. It is, however, the basic reproduction number for a typical community, with some history of exposure to circulating strains of influenza, that is most relevant to planning for the control of pandemic influenza and it is this ‘basic’ reproduction number that we use here.
v. The current fear of an influenza pandemic stems from avian influenza, specifically that re-assortment might occur if an individual is infected with both the avian influenza virus and a human influenza virus. The possibility that this would lead to a virus that is much more transmissible than a currently circulating human influenza virus seems a less likely scenario.
Individually, each of these observations can be explained in a way that is consistent with a larger value of R0, but collectively they suggest that the range 1.5-3.5 seems to cover the most plausible range for the basic reproduction number against which interventions ought to be evaluated.
The range of values 1.5-3.5 also covers the range of attack rates that are of greatest concern. In most of our illustrative calculations we used the three values 1.5, 2.5 and 3.5 for R0. We may view these as the low, medium and high values of R0 because, for a community consisting of homogeneous individuals who mix uniformly, the SEIR model gives attack rates of influenza infection of 58%, 89% and 97%, respectively, for these values of R0.