Generalization of the immigration and the stable population model

Building upon an idea presented by Espenshade, Bouvier and Arthur (1982) about the eventual stationarity of a population subjected to a net reproduction rate of less than one and a constant stream of immigration, this note reports the consequences upon the birth trajectory for all possible values of the net reproduction rate. It has been shown that when the net reproduction rate is equal to one, the number of births increases linearly with time. As may be expected, the increase is exponential for values of net reproduction rate greater than one.