Definition and estimation of an actual reproduction number describing past infectious disease transmission: application to HIV epidemics among homosexual men in Denmark, Norway and Sweden

Prevalence and incidence measures are the common way to describe epidemics. The reproduction number supplies information on the potential for growth or decline of an epidemic. We define an actual reproduction number for infectious disease transmission that has taken place. An estimator is suggested, based on the number of new infections observed in a given time-interval, the number of those infected at the start of the interval, and the length of the infectious period. That estimator is applied to HIV among men having sex with other men over the period, 1977-1995, in Scandinavia. The actual reproduction number was estimated with acceptable certainty from the period, 1981-1982, yielding a value or 15 secondary cases. A value of less than one secondary case was assessed for the period, 1988-1995, in Denmark and Sweden. The actual reproduction number gives us some additional understanding of the dynamics of epidemics, compared with prevalence and incidence curves.