Volume 4, Issue 2, June 2019, Page: 22-35
Modeling the Effects of Contraceptives as a Control Strategy in Human Population Dynamics
Kirui Wesley, Department of Mathematics and Actuarial Science, South Eastern Kenya University, Kitui, Kenya
Rotich Titus, Department of Mathematics and Physics, Moi University, Eldoret, Kenya
Received: Jun. 15, 2019;       Accepted: Jul. 22, 2019;       Published: Aug. 16, 2019
DOI: 10.11648/j.mma.20190402.12      View  111      Downloads  32
The population size of every country or government is very important in planning on effective service delivery. The cost of conducting population census yearly is of great significance to the country’s budget and many countries conduct population census once in a decade. This makes planning and provision of services to be based on mere approximation. Provision of free maternity services, estimation of national hospital insurance fund premium for medical care, and provision of retirement benefits, payment of allowances to the aged require accurate demographic statistics. In this study, population dynamics is described using a stochastic model, where population is put into distinct and disjoint age classes: Juvenile, sub-Adult, Adult, Resting-Adult, Senior Citizens and the Aged. These structures are assigned intra and inter group transmission rates which form the elements of transmission matrix and presented in form of a Leslie model. The model was modified to allow stochastic variation of transition parameters which is affected by demographic and environmental factors, specifically the effect of contraceptives to control population. It was found that intermittent implementation of control strategy at 50% and 70% efficacy yields a steady population growth rate of λ=1.39 and a steady population distribution of P=(23%, 10%, 23%, 18%, 23%, 20%, 6%)T.
Population Control, Employment Ratio, Replacement Rate, Economic Ratio, Force Dependency Ratio, Leslie Model, Dependency Ratio, Demographic Parameters
To cite this article
Kirui Wesley, Rotich Titus, Modeling the Effects of Contraceptives as a Control Strategy in Human Population Dynamics, Mathematical Modelling and Applications. Vol. 4, No. 2, 2019, pp. 22-35. doi: 10.11648/j.mma.20190402.12
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
W. C. ALLEE, Co-operation among animals, American Journal of Sociology, 37 (1931), pp. 386-398.
ANTHENA MAKROGLOU, JIAXU LI and Y. KUANG, Mathematical models and software tools for the glucose-insulin regulatory system and diabetes: an overview, Applied Numerical Mathemaics, 56 (2006), pp. 559-573.
O. O. APENTENG, Demographic Modelling of Human Population Growth, LAPPEENRANTA UNIVERSITY OF TECHNOLOGY, 2009.
S. -L. CHUANG, The stochastic mortality modeling and the pricing of mortality/longevity linked derivatives, 2013.
P. COX, Mathematical Models for the Growth of Human Populations. By JH Pollard. [Pp. xii+ 186. Cambridge University Press, 1973. £ 5. 80.] Population Dynamics. Edited by TNE Greville. [Pp. ix+ 445. Academic Press, London, 1972. £ 6. 75.], (1973).
L. EULER, A general investigation into the mortality and multiplication of the human species, Theoretical Population Biology, 1 (1970), pp. 307-314.
D. GONZE, Discrete age-structured models: The Leslie matrices, (2015).
L. A. GOODMAN, An elementary approach to the population projection-matrix, to the population reproductive value, and to related topics in the mathematical theory of population growth, Demography, 5 (1968), pp. 382-409.
M. GUILLOT, The effect of changes in fertility on the age distribution of stable populations, Demographic Research, 20 (2009), pp. 595-598.
H. HAARIO, E. SAKSMAN and J. TAMMINEN, An adaptive Metropolis algorithm, Bernoulli (2001), pp. 223-242.
D. HANSEL, G. MATO, C. MEUNIER and L. NELTNER, On numerical simulations of integrate-and-fire neural networks, Neural Computation, 10 (1998), pp. 467-483.
M. KOT, Elements of mathematical ecology, Cambridge University Press, 2001.
L. LEFKOVITCH, The study of population growth in organisms grouped by stages, Biometrics (1965), pp. 1-18.
P. H. LESLIE, On the use of matrices in certain population mathematics, Biometrika, 33 (1945), pp. 183-212.
P. H. LESLIE, Some further notes on the use of matrices in population mathematics, Biometrika, 35 (1948), pp. 213-245.
T. R. MALTHUS, An Essay on the Principle of Population, as it Affects the Future Imporvement of Society, with Remarks on the Speculations of Mr. Godwin, M. Condorcet, and Other Writers, The Lawbook Exchange, Ltd., 1798.
W. J. MEYER, Concepts of mathematical modeling, Courier Corporation, 2012.
D. M. MORENS, G. K. FOLKERS and A. S. FAUCI, The challenge of emerging and re-emerging infectious diseases, Nature, 430 (2004), pp. 242-249.
W. H. ORGANIZATION, The world health report 2000: health systems: improving performance, World Health Organization, 2000.
W. E. RICKER, Computation and interpretation of biological statistics of fish populations, Bull. Fish. Res. Bd. Can., 191 (1975), pp. 1-382.
F. M. SCUDO, Vito Volterra and theoretical ecology, Theoretical population biology, 2 (1971), pp. 1-23.
L. SIGLER, Fibonacci’s Liber Abaci: a translation into modern English of Leonardo Pisano’s book of calculation, Springer Science & Business Media, 2003.
A. TSOULARIS and J. WALLACE, Analysis of logistic growth models, Mathematical biosciences, 179 (2002), pp. 21-55.
M. B. USHER, Developments in the Leslie matrix model, Mathematical models in ecology (1972), pp. 29-60.
M. B. USHER, A matrix approach to the management of renewable resources, with special reference to selection forests, Journal of Applied Ecology (1966), pp. 355-367.
P. -F. VERHULST, Notice sur la loi que la population suit dans son accroissement. correspondance mathématique et physique publiée par a, Quetelet, 10 (1838), pp. 113-121.
M. WILLIAMSON, Some extensions of the use of matrices in population theory, Bulletin of Mathematical Biology, 21 (1959), pp. 13-17.
J. WU and O. L. LOUCKS, From balance of nature to hierarchical patch dynamics: a paradigm shift in ecology, The Quarterly review of biology, 70 (1995), pp. 439-466.
http://listcrux.com/10-effective-ways-to-control-population/ Accessed on 28th July 2016, at 12.21pm
https://www.theguardian.com/global-development/datablog/2013/dec/12/kenya-how-changed-independence-data. Accessed on 28/07/2016 at 1. 30pm
http://databank.worldbank.org/data/reports.aspx?source=2&series=SP. DYN. LE 00. IN &country=#. Accessed on 28/07/2016 at 1. 42p.
Browse journals by subject