Optimal Control Strategy for the Transmission Dynamics of Typhoid Fever

Temesgen Debas Awoke

doi:doi:10.11648/j.ajam.20190702.11

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Optimal Control Strategy for the Transmission Dynamics of Typhoid Fever

Temesgen Debas Awoke

Published in American Journal of Applied Mathematics (Volume 7, Issue 2)

Received: 13 April 2019 Accepted: 28 May 2019 Published: 26 June 2019

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Abstract

The author developed a deterministic mathematical model for Typhoid fever disease dynamics that accounts for Vaccination and relapse of treatment. Three control strategies (vaccination, treatment of infection, screening and treatment of carriers) are applied to investigate the optimal intervention strategy of controlling Typhoid disease transmission. The aim of this study is to determine the optimal combination strategy of vaccination, treatment of infection, screening and treatment of carriers that will minimize the cost of those strategies and the number of Infective and Carriers. The author used Pontryagin’s maximum principle to characterize the optimal level of those three strategies. The result is simulated numerically using Runge-Kutta fourth order method through MATLAB software. Numerical results showed that implementation of all controls or a combination of vaccination, treatment of invectives as well as screening and treatment of carriers is the best strategy to eradicate the disease at an optimal level with minimum cost of interventions.

Published in	American Journal of Applied Mathematics (Volume 7, Issue 2)
DOI	10.11648/j.ajam.20190702.11
Page(s)	37-48
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

"Typhoid Fever, Optimal Control, Pontryagin Maximum Principle, Equilibrium Point, Basic Reproduction Number, Numerical Simulation "

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APA Style

Temesgen Debas Awoke. (2019). Optimal Control Strategy for the Transmission Dynamics of Typhoid Fever. American Journal of Applied Mathematics, 7(2), 37-48. https://doi.org/10.11648/j.ajam.20190702.11

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ACS Style

Temesgen Debas Awoke. Optimal Control Strategy for the Transmission Dynamics of Typhoid Fever. Am. J. Appl. Math. 2019, 7(2), 37-48. doi: 10.11648/j.ajam.20190702.11

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AMA Style

Temesgen Debas Awoke. Optimal Control Strategy for the Transmission Dynamics of Typhoid Fever. Am J Appl Math. 2019;7(2):37-48. doi: 10.11648/j.ajam.20190702.11

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@article{10.11648/j.ajam.20190702.11,
  author = {Temesgen Debas Awoke},
  title = {Optimal Control Strategy for the Transmission Dynamics of Typhoid Fever},
  journal = {American Journal of Applied Mathematics},
  volume = {7},
  number = {2},
  pages = {37-48},
  doi = {10.11648/j.ajam.20190702.11},
  url = {https://doi.org/10.11648/j.ajam.20190702.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20190702.11},
  abstract = {The author developed a deterministic mathematical model for Typhoid fever disease dynamics that accounts for Vaccination and relapse of treatment. Three control strategies (vaccination, treatment of infection, screening and treatment of carriers) are applied to investigate the optimal intervention strategy of controlling Typhoid disease transmission. The aim of this study is to determine the optimal combination strategy of vaccination, treatment of infection, screening and treatment of carriers that will minimize the cost of those strategies and the number of Infective and Carriers. The author used Pontryagin’s maximum principle to characterize the optimal level of those three strategies. The result is simulated numerically using Runge-Kutta fourth order method through MATLAB software. Numerical results showed that implementation of all controls or a combination of vaccination, treatment of invectives as well as screening and treatment of carriers is the best strategy to eradicate the disease at an optimal level with minimum cost of interventions.},
 year = {2019}
}

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TY  - JOUR
T1  - Optimal Control Strategy for the Transmission Dynamics of Typhoid Fever
AU  - Temesgen Debas Awoke
Y1  - 2019/06/26
PY  - 2019
N1  - https://doi.org/10.11648/j.ajam.20190702.11
DO  - 10.11648/j.ajam.20190702.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 37
EP  - 48
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20190702.11
AB  - The author developed a deterministic mathematical model for Typhoid fever disease dynamics that accounts for Vaccination and relapse of treatment. Three control strategies (vaccination, treatment of infection, screening and treatment of carriers) are applied to investigate the optimal intervention strategy of controlling Typhoid disease transmission. The aim of this study is to determine the optimal combination strategy of vaccination, treatment of infection, screening and treatment of carriers that will minimize the cost of those strategies and the number of Infective and Carriers. The author used Pontryagin’s maximum principle to characterize the optimal level of those three strategies. The result is simulated numerically using Runge-Kutta fourth order method through MATLAB software. Numerical results showed that implementation of all controls or a combination of vaccination, treatment of invectives as well as screening and treatment of carriers is the best strategy to eradicate the disease at an optimal level with minimum cost of interventions.
VL  - 7
IS  - 2
ER  -

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Author Information

Temesgen Debas Awoke

Department of Mathematics, College of Natural and Computational Science, Kotebe Metropolitan University, Addis Ababa, Ethiopia

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APA Style

Temesgen Debas Awoke. (2019). Optimal Control Strategy for the Transmission Dynamics of Typhoid Fever. American Journal of Applied Mathematics, 7(2), 37-48. https://doi.org/10.11648/j.ajam.20190702.11

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ACS Style

Temesgen Debas Awoke. Optimal Control Strategy for the Transmission Dynamics of Typhoid Fever. Am. J. Appl. Math. 2019, 7(2), 37-48. doi: 10.11648/j.ajam.20190702.11

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AMA Style

Temesgen Debas Awoke. Optimal Control Strategy for the Transmission Dynamics of Typhoid Fever. Am J Appl Math. 2019;7(2):37-48. doi: 10.11648/j.ajam.20190702.11

Copy | Download

@article{10.11648/j.ajam.20190702.11,
  author = {Temesgen Debas Awoke},
  title = {Optimal Control Strategy for the Transmission Dynamics of Typhoid Fever},
  journal = {American Journal of Applied Mathematics},
  volume = {7},
  number = {2},
  pages = {37-48},
  doi = {10.11648/j.ajam.20190702.11},
  url = {https://doi.org/10.11648/j.ajam.20190702.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20190702.11},
  abstract = {The author developed a deterministic mathematical model for Typhoid fever disease dynamics that accounts for Vaccination and relapse of treatment. Three control strategies (vaccination, treatment of infection, screening and treatment of carriers) are applied to investigate the optimal intervention strategy of controlling Typhoid disease transmission. The aim of this study is to determine the optimal combination strategy of vaccination, treatment of infection, screening and treatment of carriers that will minimize the cost of those strategies and the number of Infective and Carriers. The author used Pontryagin’s maximum principle to characterize the optimal level of those three strategies. The result is simulated numerically using Runge-Kutta fourth order method through MATLAB software. Numerical results showed that implementation of all controls or a combination of vaccination, treatment of invectives as well as screening and treatment of carriers is the best strategy to eradicate the disease at an optimal level with minimum cost of interventions.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Optimal Control Strategy for the Transmission Dynamics of Typhoid Fever
AU  - Temesgen Debas Awoke
Y1  - 2019/06/26
PY  - 2019
N1  - https://doi.org/10.11648/j.ajam.20190702.11
DO  - 10.11648/j.ajam.20190702.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 37
EP  - 48
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20190702.11
AB  - The author developed a deterministic mathematical model for Typhoid fever disease dynamics that accounts for Vaccination and relapse of treatment. Three control strategies (vaccination, treatment of infection, screening and treatment of carriers) are applied to investigate the optimal intervention strategy of controlling Typhoid disease transmission. The aim of this study is to determine the optimal combination strategy of vaccination, treatment of infection, screening and treatment of carriers that will minimize the cost of those strategies and the number of Infective and Carriers. The author used Pontryagin’s maximum principle to characterize the optimal level of those three strategies. The result is simulated numerically using Runge-Kutta fourth order method through MATLAB software. Numerical results showed that implementation of all controls or a combination of vaccination, treatment of invectives as well as screening and treatment of carriers is the best strategy to eradicate the disease at an optimal level with minimum cost of interventions.
VL  - 7
IS  - 2
ER  -

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