On the biological interpretation of a definition for the parameter R0 in periodic population models

An adaptation of the definition of the basic reproduction number R 0 to time-periodic seasonal models was suggested a few years ago. However, its biological interpretation remained unclear. The present paper shows that in demography, this R 0 is the asymptotic ratio of total births in two successive generations of the family tree. In epidemiology, it is the asymptotic ratio of total infections in two successive generations of the infection tree. This result is compared with other recent work.