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A study of a Malthusian parameter in relation to some stochastic models of human reproduction
Journal article   Peer reviewed

A study of a Malthusian parameter in relation to some stochastic models of human reproduction

Charles J. Mode
Theoretical population biology, v 3(3), pp 300-323
1972
DOI: https://doi.org/10.1016/0040-5809(72)90006-8
PMID: 4667089

Abstract

The paper is divided into six sections and is devoted to a study of a Malthusian parameter in relation to some stochastic models of human reproduction. In Section 1, some of the motivations underlying the study are discussed, and in Section 2 some literature on the stochastic model of population growth underlying the foundations of the paper is briefly reviewed. Section 3, which lays the foundations for the study of a more complicated model in Section 4, is devoted to the study of the Malthusian parameter in relation to a stochastic model of human reproduction formulated as a terminating renewal process. In Section 4 the Malthusian parameter is studied in relation to a terminating Markov renewal model of human reproduction, stemming from the work of Perrin and Sheps (1964). Among the mathematical results of independent interest in this section is a complete spectral decomposition of the Laplace-Stieltjes transform of the semi-Markov transition matrix in the model of Perrin and Sheps. Section 5 is devoted to the discussion of a mathematical method which allows accomodating in the model the time taken by an individual to reach reproductive age, and Section 6 ends the paper by supplying bounds for the Malthusian parameter which are valid under quite general conditions. Possible applications of the results in evaluating what influences a population policy may have on population growth are also discussed.

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