Functional differential equations and age dependent population growth

Abstract

Growth equations are established for a population of individuals that have fixed age dependent reproduction and mortality rates. Equations are obtained both for the population density and for the numerical size of the population in a fixed age group. Age and time dependent migration is taken into consideration. The usual integral equation of renewal type for these variables is shown to be equivalent to a functional differential equation of retarded type; these differential equations are of main interest in this work. The role of initial data in characterizing a unique solution of the functional differential equation is examined in detail. Finally, some special cases for the reproduction and mortality rates are considered where the functional differential equations take a reasonably simple form.