Some further results from a stochastic fertility model for women

Abstract

Any realistic model of human fertility should encompass the distributions and interactions of three time intervals a fecund married woman may experience repeatedly in her childbearing period: (1) waiting time for a conception, (2) gestation period, and (3) period of postpartum amenorrhea. Perrin & Sheps (1964) presented a model in which human reproduction is viewed as a Markov renewal process with a finite number of states. Das Gupta (1973 b) presented a general probability model of fertility along the lines suggested by Perrin & Sheps which removes two limitations of their model. First, it does not assume that the distributions of durations of stay in the fertility states are independent of each other. Second, it allows us to study the effect of breast-feeding on demographic characteristics, such as interval between live births or birth rate. Results derived in Das Gupta (1973 b) include the distributions of time intervals and the exact probabilities of different states at a particular time. The present paper includes additional results pertaining to the same general model, such as the distribution of number of conceptions in a fixed period of time, the distribution of time needed for a fixed number of conceptions, pregnancy rate and fertility rate, and the distribution of the time elapsed since last live birth. The general results are applied to specific models to obtain some known results.