A stochastic model of human reproduction: some preliminary results

The stochastic model of human reproduction presented in this paper removes some of the limitations of the Perrin—Sheps model. It considers the possibility of dependence of amenorrhea period on the preceding gestation period, and also for live births, on the breast-feeding practices of the mother. Two models, virtually identical in concepts, are considered depending on whether time is treated as a continuous or discrete variable. The basic distributions in the models are kept arbitrary, and, therefore, the results for all the existing homogeneous fertility models can be obtained directly from the general results as special cases. The results presented here include the distribution of the interval between two live births, and the probabilities of different states at a point in time. We also illustrate the applications of the models to special cases and generate many known results.