Planning for the mitigation and control of such health threats relies increasingly on mathematical models of infection transmission. 2003) and the risk of an influenza pandemic among human populations ( Longini et al. 2001), the fear of bioterrorist attacks with smallpox virus ( Gani & Leach 2001), the emergence of severe acute respiratory syndrome (SARS) in 2003 ( Lipsitch et al. This is due in part to disease outbreaks in domestic livestock ( Keeling et al. The past decade has seen a dramatic increase in the attention paid to infectious disease epidemics as a potential health threat. Furthermore, we show that by taking the generation interval distribution equal to the observed distribution, it is possible to obtain an empirical estimate of the reproductive number. We show that by assuming all generation intervals to be equal to the mean, we obtain an upper bound to the range of possible values that the reproductive number may attain for a given growth rate.

Therefore, the shape of the generation interval distribution determines which equation is appropriate for inferring the reproductive number from the observed growth rate. Here, we show that these different equations differ only with respect to their assumed shape of the generation interval distribution. Such inference is ambiguous as several different equations exist that relate the reproductive number to the growth rate, and it is unclear which of these equations might apply to a new infection. For new emerging infectious diseases, the value of the reproductive number can only be inferred indirectly from the observed exponential epidemic growth rate r. A key variable in such models is the reproductive number R. Mathematical models of transmission have become invaluable management tools in planning for the control of emerging infectious diseases.

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