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The asymptotic behaviour due to a piecewise time dependent net maternity function

Published online by Cambridge University Press:  17 February 2009

P. Cerone  and
K. P. Tognetti
P. Cerone
Affiliation:
Department of Mathematics, The University of Wollongong, Box 1144, Wollongong, N.S.W. 2500
K. P. Tognetti
Affiliation:
Department of Mathematics, The University of Wollongong, Box 1144, Wollongong, N.S.W. 2500
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Abstract

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The long term asymptotic behaviour of a population is evaluated where the age specific fertility behaviour is allowed to change with time. Thus in this article the behaviour of a population is determined with a time dependent net maternity function. It is shown that methods used when the net maternity function was independent of time are still applicable if the change with time is explicit only for the initial population. Further, using the fact that for realistic situations the net maternity function is non-zero over a finite interval α < x < β, it is shown that traditional methods can again be used if the time dependence is associated with ages less than α, the minimum age of childbearing. Recent extensions of Cerone and Keane to include exponential time dependence are utilized and models are presented which are piecewise defined, allowing general and exponential time dependence for the parent and new-born populations respectively. The Sharpe-Lotka single sex determinstic population model is used as the basis for the analysis.

Type
Research Article
Information
The ANZIAM Journal , Volume 23 , Issue 4 , April 1982 , pp. 438 - 450
Copyright
Copyright © Australian Mathematical Society 1982

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