On a model for population with age structure

Abstract

In this paper we study a linear continuous model describing age structure into a dynamics of one sex population, related with the McKendrick model. McKendrick assumes that the female population can be described by a function of two variables, age and time. Using the method of characteristics and Laplace transform, it is possible to find the function representing the number of births in unit time t and the total population size in some particular cases. In the content of some works referring to the behavior of age-structure one sex population is presented the complete model of the Lotka-McKendrick equation given in the system (5) for simple cases. The genesis model is a simple one that works with the Dirac distribution and it is presented in [1]. When the birth modulus is given by the relation (9), we determine the differential-difference equation for the function B(t) which represents the number of births in unit time, given in (3).