Modeling the Effects of Contraceptives as a Control Strategy in Human Population Dynamics

Kirui Wesley; Rotich Titus

doi:doi:10.11648/j.mma.20190402.12

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Modeling the Effects of Contraceptives as a Control Strategy in Human Population Dynamics

Kirui Wesley, Rotich Titus

Published in Mathematical Modelling and Applications (Volume 4, Issue 2)

Received: 15 June 2019 Accepted: 22 July 2019 Published: 16 August 2019

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Abstract

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.

Published in	Mathematical Modelling and Applications (Volume 4, Issue 2)
DOI	10.11648/j.mma.20190402.12
Page(s)	22-35
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Population Control, Employment Ratio, Replacement Rate, Economic Ratio, Force Dependency Ratio, Leslie Model, Dependency Ratio, Demographic Parameters

References

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APA Style

Kirui Wesley, Rotich Titus. (2019). Modeling the Effects of Contraceptives as a Control Strategy in Human Population Dynamics. Mathematical Modelling and Applications, 4(2), 22-35. https://doi.org/10.11648/j.mma.20190402.12

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ACS Style

Kirui Wesley; Rotich Titus. Modeling the Effects of Contraceptives as a Control Strategy in Human Population Dynamics. Math. Model. Appl. 2019, 4(2), 22-35. doi: 10.11648/j.mma.20190402.12

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AMA Style

Kirui Wesley, Rotich Titus. Modeling the Effects of Contraceptives as a Control Strategy in Human Population Dynamics. Math Model Appl. 2019;4(2):22-35. doi: 10.11648/j.mma.20190402.12

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@article{10.11648/j.mma.20190402.12,
  author = {Kirui Wesley and Rotich Titus},
  title = {Modeling the Effects of Contraceptives as a Control Strategy in Human Population Dynamics},
  journal = {Mathematical Modelling and Applications},
  volume = {4},
  number = {2},
  pages = {22-35},
  doi = {10.11648/j.mma.20190402.12},
  url = {https://doi.org/10.11648/j.mma.20190402.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20190402.12},
  abstract = {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.},
 year = {2019}
}

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TY  - JOUR
T1  - Modeling the Effects of Contraceptives as a Control Strategy in Human Population Dynamics
AU  - Kirui Wesley
AU  - Rotich Titus
Y1  - 2019/08/16
PY  - 2019
N1  - https://doi.org/10.11648/j.mma.20190402.12
DO  - 10.11648/j.mma.20190402.12
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 22
EP  - 35
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20190402.12
AB  - 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.
VL  - 4
IS  - 2
ER  -

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Author Information

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

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Plain Text BibTeX RIS

APA Style

Kirui Wesley, Rotich Titus. (2019). Modeling the Effects of Contraceptives as a Control Strategy in Human Population Dynamics. Mathematical Modelling and Applications, 4(2), 22-35. https://doi.org/10.11648/j.mma.20190402.12

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ACS Style

Kirui Wesley; Rotich Titus. Modeling the Effects of Contraceptives as a Control Strategy in Human Population Dynamics. Math. Model. Appl. 2019, 4(2), 22-35. doi: 10.11648/j.mma.20190402.12

Copy | Download

AMA Style

Kirui Wesley, Rotich Titus. Modeling the Effects of Contraceptives as a Control Strategy in Human Population Dynamics. Math Model Appl. 2019;4(2):22-35. doi: 10.11648/j.mma.20190402.12

Copy | Download

@article{10.11648/j.mma.20190402.12,
  author = {Kirui Wesley and Rotich Titus},
  title = {Modeling the Effects of Contraceptives as a Control Strategy in Human Population Dynamics},
  journal = {Mathematical Modelling and Applications},
  volume = {4},
  number = {2},
  pages = {22-35},
  doi = {10.11648/j.mma.20190402.12},
  url = {https://doi.org/10.11648/j.mma.20190402.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20190402.12},
  abstract = {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.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Modeling the Effects of Contraceptives as a Control Strategy in Human Population Dynamics
AU  - Kirui Wesley
AU  - Rotich Titus
Y1  - 2019/08/16
PY  - 2019
N1  - https://doi.org/10.11648/j.mma.20190402.12
DO  - 10.11648/j.mma.20190402.12
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 22
EP  - 35
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20190402.12
AB  - 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.
VL  - 4
IS  - 2
ER  -

Copy | Download