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SUMMARY A class of stochastic models to approximate the reproductive process in the human female is presented. It is assumed that at marriage a woman is in a fecundable nonpregnant state and after a random length of time passes into a pregnant state, the pregnancy terminating in a miscarriage, a stillbirth or a live birth with a given probability. Each pregnancy is followed by an infecundable state from which the female eventually returns to the fecundable, nonpregnant state. The duration of stay in any state is taken to be a random variable whose distribution can depend on the state into which the woman will pass next, as well as on the state currently occupied. Expressions are derived for the moments of all first passage and renewal times (e.g. intervals between births, etc.) and for the asymptotic monthly probability of a live birth, under the model. Approximate expressions are given for the mean and variance of the number of events, such as live births, that occur within a given period after marriage. The degree of approximation attained by the asymptotic expressions to the exact results for a finite number of months is investigated in a special case and found to be satisfactory. The model is discussed in the light of biological knowledge and references are cited, to work in which these results receive applications.
Perrin et al. (Sun,) studied this question.