The usefulness of the actual reproduction number, calculated as a product of the mean generation time and the incidence-to-prevalence ratio, has been previously emphasized in assessing the epidemiological time course of an epidemic [14, 15] . However, it appears that R a does not precisely capture the secondary transmission if the transmission rate () varies with infection-age  [18] , and moreover, the cohort-and period-reproduction numbers directly derived from the renewal equation have been suggested to be more accurate figures in capturing the underlying transmission dynamics [17, 33] . In the present study, replacing the denominator (i.e., prevalence) of R a by the total number of potential contacts, it was shown that the R 0 derived from the renewal equation coincides with the corrected actual reproduction number, R a , and also that the likelihood can be quite easily derived. The corrected R a does not require prevalence data, and uses only the incidence data and the generation time distribution.