The momentum of population growth with time dependent net maternity function

Abstract

The momentum of population growth problem of Keyfitz is generalized to contain a gradual change of the age-specific birth rate to the level of bare replacement. Assuming a time dependence for the net maternity function of the form \(\frac{1}{R} + \left( {1 - {\textstyle{1 \over R}}} \right)e^{ - \lambda t} \), R being the net reproductive rate, we show that for the Malthusian model the asymptotic birth rate is increased by exp (r/λ), where r is the rate of increase of the population before t = 0. A numerical method for obtaining the asymptotic birth rate for a general net maternity function with the same time dependence is outlined.

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References

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Cerone, P., Keane, A. The momentum of population growth with time dependent net maternity function. Demography 15, 131–134 (1978). https://doi.org/10.2307/2060495

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Keywords

  • Gradual Change
  • Total Birth Rate
  • Renewal Equation
  • Discontinuous Model
  • Desire Birth Rate