Abstract
Using the integral population model of Sharpe and Lotka, it is demonstrated that if the time variation of the maternity function is assumed to only affect the parent population, then standard methods of obtaining the long-term behavior may still be used. Further, if the net maternity function has explicit time dependence, in contrast to age dependence, only for time less than the minimum age of childbearing, the standard techniques still may be used. It is shown that the recent extensions of Cerone and Keane to include exponential time dependence may be applied, together with the above observations, to define piecewise time-dependent net maternity functions and to determine the resulting long-term asymptotic behavior of the population. The population management problem of determining the time path of change needed to approach a given population also is considered in some detail.
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References
Bellman, R. and K. L. Cooke. 1963. Differential Difference Equations. New York: Academic Press.
Cerone, P. and A. Keane. 1978a. The Momentum of Population Growth with Time Dependent Net Maternity Function. Demography 15:131–134.
— 1978b. The Stable Births Resulting from a Time Dependent Change Between Two Net Maternity Functions. Demography 15:135–137.
Coale, A. J. 1973. Atlernative Paths to a Stationary Population. Pp. 589–603 in Charles F. Westoff and Robert Parke Jr. (eds.), Demographic and Social Aspects of Population Growth. The Commission on Population Growth and the American Future Research Reports, Vol. 1. Washington, D.C: U. S. Government Printing Office.
Frauenthal, J. C. 1975. Birth Trajectory Under Changing Fertility Conditions. Demography 12:447–454.
Frejka, T. 1973. The Future of Population Growth: Alternative Paths to Equilibrium. New York: John Wiley and Sons.
Keyfitz, N. 1968. Introduction to the Mathematics of Population. Reading, Mass.: Addison-Wesley.
— 1971. On the Momentum of Population Growth. Demography 8:71–80.
— 1975. Reproductive Value: With Applications to Migration, Contraception, and Zero Population Growth. Pp. 587–612 in H. M. Blalock et al. (eds.), Quantitative Sociology: International Perspectives on Mathematical and Statistical Modeling. New York: Academic Press.
— 1977. Applied Mathematical Demography. New York: John Wiley and Sons.
Lopez, A. 1961. Problems in Stable Population Theory. Princeton: Office of Population Research, Princeton University.
Mitra, S. 1976. Influence on Instantaneous Fertility Decline to Replacement Level on Population Growth. Demography 13:513–519.
Nortman, D. and J. Bongaarts. 1975. Contraceptive Practice Required to Meet a Prescribed Crude Birth Rate Target: A Proposed Macro-Model (TABRAP) and Hypothetical Illustrations. Demography 12:471–489.
Pollard, J. H. 1973. Mathematical Models for the Growth of Human Populations. Cambridge: Cambridge University Press.
Ruzicka, L. T. 1977. Reflections on Zero Growth of the Australian Population. National Population Inquiry, Research Report No. 7. Canberra: Australian Government Publishing Service.
Sharpe, F. R. and A. J. Lotka. 1911. A Problem in Age-Distribution. Philosophical Magazine 21:435–438.
Tognetti, K. P. 1976. Some Extensions of the Keyfitz Momentum Relationship. Demography 13:507–512.
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Cerone, P. The long-term effects of time-dependent maternity behavior. Demography 20, 79–86 (1983). https://doi.org/10.2307/2060902
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DOI: https://doi.org/10.2307/2060902