Human population reproduction via first marriage

In this paper we consider a dynamical model for populations in which childbearing occurs within only first marriage. Instead of age‐specific fertility rate, we use duration‐specific marital fertility rate by age at marriage. The basic model is formulated as a partial differential equation system with integral boundary condition. By solving the system, we will show the strong ergodic properties for our model. Next we introduce the basic reproduction number R0 that measures the reproductivity of the population. We further give a new formula for total fertility rate, which is expressed by an integral of the product of the indices of marriage and marital fertility. Subsequently, we show illustrative calculations to see the effect of nuptiality on the reproductivity indices. Finally we discuss a possible interpretation for the recent Japanese fertility decline as an application of our first marriage model.

Key words:

• First marriage model
• marital fertility
• nuptiality
• basic reproduction number
• total fertility rate
• reproductivity