Abstract
The discrete time recurrence model and the continuous time model which were discussed in Chapters Three and Four focused on the births that occurred at a particular time and their relationship to the births that occurred prior to this time. In each case the age distribution of the population was discussed almost as an adjunct to the model and not as an integral part of it. Perhaps this was unfortunate since it was the asymptotic age distribution of the model that gave meaning to the concept of a ‘stable’ population.
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Notes for Chapter Five
Bernardelli, H. (1941), Population waves. Journal of the Burma Research Society, vol. 31, part 1, pp. 1–18.
Lewis, E.G. (1942), On the generation and growth of a population. Sank- hya, vol. 6, pp. 93–96.
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Ibid., p. 187.
Ibid., p. 187.
Gantmacher, F.R. (1959), Applications of the theory of matrices, p. 61.
Perron, O. (1907), Zur Theorie der Matrizen. Mathematische Annalen, vol. 64, p. 248 ff.
Frobenius, G. (1912), Über Matrizen aus nicht negativen Elementen. Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften, Berlin, p. 456ff.
Gantmacher, op. cit., p. 64 ff.
Ibid., p.
Meyer, W. (1982), Asymptotic birth trajectories in the discrete form of stable population theory. Theoretical Population Biology, vol. 21, no. 2, pp. 167–170.
The development of this section is primarily due to the invention of the author.
Moore, John T. (1968), Elements of linear algebra and matrix theory, p. 327 ff.
Noble, Ben (1969), Applied linear algebra, p. 361 ff.
Pollard, J.H. (1973), Mathematical models for the growth of human populations, pp. 44–45.
Noble, Ben, op. cit., pp. 363–366.
Lefkovitch, L.P. (1965), The study of population growth in organisms grouped by stages. Biometrics, vol. 21, pp. 1–18.
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Impagliazzo, J. (1985). The Discrete Time Matrix Model. In: Deterministic Aspects of Mathematical Demography. Biomathematics, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82319-0_5
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DOI: https://doi.org/10.1007/978-3-642-82319-0_5
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