Epidemiological Modeling of Measles Infection with Optimal Control of Vaccination and Supportive Treatment

Okey Oseloka Onyejekwe; Esayas Zewdie Kebede

doi:doi:10.11648/j.acm.20150404.15

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Epidemiological Modeling of Measles Infection with Optimal Control of Vaccination and Supportive Treatment

Okey Oseloka Onyejekwe, Esayas Zewdie Kebede

Published in Applied and Computational Mathematics (Volume 4, Issue 4)

Received: 19 May 2015 Accepted: 9 June 2015 Published: 1 July 2015

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Abstract

We consider an SEIR model with constant population size and formulate an optimal control problem subject to vaccination and supportive treatment as controls. Our aim is to find the optimal combination of vaccination and supportive treatment strategies that will minimize the cost of the two control measures as well as the number of infectives while efficiently balancing vaccination and management of measles applied to the models with various cost scenarios. We used Pontryagin’s maximum principle to characterize the optimal levels of the two controls. The resulting optimality system is solved numerically by forward-backward sweep method. The results show that the optimal combination of the strategies required to achieve the set objective will depend on the relative cost of each of the control measures and the resulting optimality system showed that, the use of vaccinating and supportive treating at the same time at the highest possible rate to the population as early as possible is essential for controlling measles epidemic. The results from our simulation are discussed.

Published in	Applied and Computational Mathematics (Volume 4, Issue 4)
DOI	10.11648/j.acm.20150404.15
Page(s)	264-274
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), 2015. Published by Science Publishing Group

Keywords

Measles, Optimal Control, Pontryagin’s Maximum Principle, Adjoint Condition, Transversality Condition, Hamiltonian, Optimality System

References

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[13]	Ethiopian health and nutrition research institute federal democratic republic of Ethiopia - Guideline on Measles Surveillance and Outbreak Management, January 2012.
[14]	H. Trottier, P. Philippe. Deterministic Modeling of Infectious Diseases: Applications To Measles And Other Similar Infections. The Internet Journal of Infectious Diseases, Volume 2 Number 1, 2001.
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APA Style

Okey Oseloka Onyejekwe, Esayas Zewdie Kebede. (2015). Epidemiological Modeling of Measles Infection with Optimal Control of Vaccination and Supportive Treatment. Applied and Computational Mathematics, 4(4), 264-274. https://doi.org/10.11648/j.acm.20150404.15

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ACS Style

Okey Oseloka Onyejekwe; Esayas Zewdie Kebede. Epidemiological Modeling of Measles Infection with Optimal Control of Vaccination and Supportive Treatment. Appl. Comput. Math. 2015, 4(4), 264-274. doi: 10.11648/j.acm.20150404.15

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AMA Style

Okey Oseloka Onyejekwe, Esayas Zewdie Kebede. Epidemiological Modeling of Measles Infection with Optimal Control of Vaccination and Supportive Treatment. Appl Comput Math. 2015;4(4):264-274. doi: 10.11648/j.acm.20150404.15

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@article{10.11648/j.acm.20150404.15,
  author = {Okey Oseloka Onyejekwe and Esayas Zewdie Kebede},
  title = {Epidemiological Modeling of Measles Infection with Optimal Control of Vaccination and Supportive Treatment},
  journal = {Applied and Computational Mathematics},
  volume = {4},
  number = {4},
  pages = {264-274},
  doi = {10.11648/j.acm.20150404.15},
  url = {https://doi.org/10.11648/j.acm.20150404.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150404.15},
  abstract = {We consider an SEIR model with constant population size and formulate an optimal control problem subject to vaccination and supportive treatment as controls. Our aim is to find the optimal combination of vaccination and supportive treatment strategies that will minimize the cost of the two control measures as well as the number of infectives while efficiently balancing vaccination and management of measles applied to the models with various cost scenarios. We used Pontryagin’s maximum principle to characterize the optimal levels of the two controls. The resulting optimality system is solved numerically by forward-backward sweep method. The results show that the optimal combination of the strategies required to achieve the set objective will depend on the relative cost of each of the control measures and the resulting optimality system showed that, the use of vaccinating and supportive treating at the same time at the highest possible rate to the population as early as possible is essential for controlling measles epidemic. The results from our simulation are discussed.},
 year = {2015}
}

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TY  - JOUR
T1  - Epidemiological Modeling of Measles Infection with Optimal Control of Vaccination and Supportive Treatment
AU  - Okey Oseloka Onyejekwe
AU  - Esayas Zewdie Kebede
Y1  - 2015/07/01
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20150404.15
DO  - 10.11648/j.acm.20150404.15
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 264
EP  - 274
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20150404.15
AB  - We consider an SEIR model with constant population size and formulate an optimal control problem subject to vaccination and supportive treatment as controls. Our aim is to find the optimal combination of vaccination and supportive treatment strategies that will minimize the cost of the two control measures as well as the number of infectives while efficiently balancing vaccination and management of measles applied to the models with various cost scenarios. We used Pontryagin’s maximum principle to characterize the optimal levels of the two controls. The resulting optimality system is solved numerically by forward-backward sweep method. The results show that the optimal combination of the strategies required to achieve the set objective will depend on the relative cost of each of the control measures and the resulting optimality system showed that, the use of vaccinating and supportive treating at the same time at the highest possible rate to the population as early as possible is essential for controlling measles epidemic. The results from our simulation are discussed.
VL  - 4
IS  - 4
ER  -

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Author Information

Okey Oseloka Onyejekwe

Computational Science Program, Addis Ababa University, Arat Kilo Campus, Addis Ababa Ethiopia
Esayas Zewdie Kebede

Computational Science Program, Addis Ababa University, Arat Kilo Campus, Addis Ababa Ethiopia

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Plain Text BibTeX RIS

APA Style

Okey Oseloka Onyejekwe, Esayas Zewdie Kebede. (2015). Epidemiological Modeling of Measles Infection with Optimal Control of Vaccination and Supportive Treatment. Applied and Computational Mathematics, 4(4), 264-274. https://doi.org/10.11648/j.acm.20150404.15

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ACS Style

Okey Oseloka Onyejekwe; Esayas Zewdie Kebede. Epidemiological Modeling of Measles Infection with Optimal Control of Vaccination and Supportive Treatment. Appl. Comput. Math. 2015, 4(4), 264-274. doi: 10.11648/j.acm.20150404.15

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AMA Style

Okey Oseloka Onyejekwe, Esayas Zewdie Kebede. Epidemiological Modeling of Measles Infection with Optimal Control of Vaccination and Supportive Treatment. Appl Comput Math. 2015;4(4):264-274. doi: 10.11648/j.acm.20150404.15

Copy | Download

@article{10.11648/j.acm.20150404.15,
  author = {Okey Oseloka Onyejekwe and Esayas Zewdie Kebede},
  title = {Epidemiological Modeling of Measles Infection with Optimal Control of Vaccination and Supportive Treatment},
  journal = {Applied and Computational Mathematics},
  volume = {4},
  number = {4},
  pages = {264-274},
  doi = {10.11648/j.acm.20150404.15},
  url = {https://doi.org/10.11648/j.acm.20150404.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150404.15},
  abstract = {We consider an SEIR model with constant population size and formulate an optimal control problem subject to vaccination and supportive treatment as controls. Our aim is to find the optimal combination of vaccination and supportive treatment strategies that will minimize the cost of the two control measures as well as the number of infectives while efficiently balancing vaccination and management of measles applied to the models with various cost scenarios. We used Pontryagin’s maximum principle to characterize the optimal levels of the two controls. The resulting optimality system is solved numerically by forward-backward sweep method. The results show that the optimal combination of the strategies required to achieve the set objective will depend on the relative cost of each of the control measures and the resulting optimality system showed that, the use of vaccinating and supportive treating at the same time at the highest possible rate to the population as early as possible is essential for controlling measles epidemic. The results from our simulation are discussed.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Epidemiological Modeling of Measles Infection with Optimal Control of Vaccination and Supportive Treatment
AU  - Okey Oseloka Onyejekwe
AU  - Esayas Zewdie Kebede
Y1  - 2015/07/01
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20150404.15
DO  - 10.11648/j.acm.20150404.15
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 264
EP  - 274
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20150404.15
AB  - We consider an SEIR model with constant population size and formulate an optimal control problem subject to vaccination and supportive treatment as controls. Our aim is to find the optimal combination of vaccination and supportive treatment strategies that will minimize the cost of the two control measures as well as the number of infectives while efficiently balancing vaccination and management of measles applied to the models with various cost scenarios. We used Pontryagin’s maximum principle to characterize the optimal levels of the two controls. The resulting optimality system is solved numerically by forward-backward sweep method. The results show that the optimal combination of the strategies required to achieve the set objective will depend on the relative cost of each of the control measures and the resulting optimality system showed that, the use of vaccinating and supportive treating at the same time at the highest possible rate to the population as early as possible is essential for controlling measles epidemic. The results from our simulation are discussed.
VL  - 4
IS  - 4
ER  -

Copy | Download