Optimal Control Analysis of Meningococcal Meningitis Disease with Varying Population Size

Timothy Kiprono Yano; Jacob Bitok; Rael Jerop

doi:doi:10.11648/j.acm.20221105.14

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Optimal Control Analysis of Meningococcal Meningitis Disease with Varying Population Size

Timothy Kiprono Yano, Jacob Bitok, Rael Jerop

Published in Applied and Computational Mathematics (Volume 11, Issue 5)

Received: 20 September 2022 Accepted: 4 October 2022 Published: 17 October 2022

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Abstract

Meningococcal meningitis is a fatal and scary highly infectious disease especially in the African meningitis disease belt and globally, its every community’s desire to wipe out meningitis disease by considering its prevention and control mechanisms. The paper formulates and analyzes a Meningococcal meningitis epidemic model that describes the spreading mechanisms of meningitis in a community with varying population. The stability analysis approach of non-linear systems is used to distinguish the properties of an epidemic deterministic compartmental model. The effective threshold reproductive value is determined by Jacobian approach and the stability study for the zero disease and endemic states are determined. Sensitivity indices analysis of the effective reproductive number to the crucial parameter values are established and rated accordingly. Using Pontryagin's approach to an optimal problem, the model was extended to include the following four control intervention measures: effort to prevent a disease infection by providing education needed, efforts to treat that minimizes sensitive and resistant strains and immunity control effort. The optimal control study of the applied control intervention efforts reveals that the use of prevention techniques and treatment efforts leads to a larger decrease of infections, thus becoming are the best intervention control strategy to eliminate the meningitis disease. Numerical analysis study was done for a combination of other strategies and main results are displayed using graphs.

Published in	Applied and Computational Mathematics (Volume 11, Issue 5)
DOI	10.11648/j.acm.20221105.14
Page(s)	140-149
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), 2024. Published by Science Publishing Group

Keywords

Meningococcal Meningitis, Effective Reproductive Number, Pontryagin's Principle, Optimal Intervention Strategy, Sensitivity Indices, Numerical Simulation

References

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[4]	Blyuss, K. B. (2016). Mathematical modelling of the dynamics of meningococcal meningitis in africa. In UK Success Stories in Industrial Mathematics (pp. 221-226). Springer.
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[6]	Fleming, W. H. & Rishel, R. W. (2012). Deterministic and stochastic optimal control, volume 1. Springer Science & Business Media.
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[8]	Irving, T., Blyuss, K., Colijn, C., & Trotter, C. (2012). Modelling meningococcal meningitis in the african meningitis belt. Epidemiology and Infection, 140 (5), 897-905.
[9]	Karachaliou, A., Conlan, A. J., Preziosi, M.-P., & Trotter, C. L. (2015). Modeling long-term vaccination strategies with menafrivac in the african meningitis belt. Clinical Infectious Diseases, 61 (suppl_5), S594-S600.
[10]	Mbaeyi, S. A., Bozio, C. H., Duffy, J., Rubin, L. G., Hariri, S., Stephens, D. S., & MacNeil, J. R. (2020). Meningococcal vaccination: recommendations of the advisory committee on immunization practices, united states, 2020. MMWR Recommendations and Reports, 69 (9), 1.
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[15]	Pizza, M., Bekkat-Berkani, R., & Rappuoli, R. (2020). Vaccines against meningococcal diseases. Microorganisms, 8 (10), 1521.
[16]	Pontryagin, L. S. (2018). Mathematical theory of optimal processes. Routledge.
[17]	Tilahun, G. T. (2019a). Modeling co-dynamics of pneumonia and meningitis diseases. Advances in Difference Equations, 2019 (1), 1-18.
[18]	Tilahun, G. T. (2019b). Optimal control analysis of pneumonia and meningitis coinfection. Computational and Mathematical Methods in Medicine, 2019.
[19]	Vereen, K. (2008). An scir model of meningococcal meningitis.
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APA Style

Timothy Kiprono Yano, Jacob Bitok, Rael Jerop. (2022). Optimal Control Analysis of Meningococcal Meningitis Disease with Varying Population Size. Applied and Computational Mathematics, 11(5), 140-149. https://doi.org/10.11648/j.acm.20221105.14

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ACS Style

Timothy Kiprono Yano; Jacob Bitok; Rael Jerop. Optimal Control Analysis of Meningococcal Meningitis Disease with Varying Population Size. Appl. Comput. Math. 2022, 11(5), 140-149. doi: 10.11648/j.acm.20221105.14

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AMA Style

Timothy Kiprono Yano, Jacob Bitok, Rael Jerop. Optimal Control Analysis of Meningococcal Meningitis Disease with Varying Population Size. Appl Comput Math. 2022;11(5):140-149. doi: 10.11648/j.acm.20221105.14

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@article{10.11648/j.acm.20221105.14,
  author = {Timothy Kiprono Yano and Jacob Bitok and Rael Jerop},
  title = {Optimal Control Analysis of Meningococcal Meningitis Disease with Varying Population Size},
  journal = {Applied and Computational Mathematics},
  volume = {11},
  number = {5},
  pages = {140-149},
  doi = {10.11648/j.acm.20221105.14},
  url = {https://doi.org/10.11648/j.acm.20221105.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20221105.14},
  abstract = {Meningococcal meningitis is a fatal and scary highly infectious disease especially in the African meningitis disease belt and globally, its every community’s desire to wipe out meningitis disease by considering its prevention and control mechanisms. The paper formulates and analyzes a Meningococcal meningitis epidemic model that describes the spreading mechanisms of meningitis in a community with varying population. The stability analysis approach of non-linear systems is used to distinguish the properties of an epidemic deterministic compartmental model. The effective threshold reproductive value is determined by Jacobian approach and the stability study for the zero disease and endemic states are determined. Sensitivity indices analysis of the effective reproductive number to the crucial parameter values are established and rated accordingly. Using Pontryagin's approach to an optimal problem, the model was extended to include the following four control intervention measures: effort to prevent a disease infection by providing education needed, efforts to treat that minimizes sensitive and resistant strains and immunity control effort. The optimal control study of the applied control intervention efforts reveals that the use of prevention techniques and treatment efforts leads to a larger decrease of infections, thus becoming are the best intervention control strategy to eliminate the meningitis disease. Numerical analysis study was done for a combination of other strategies and main results are displayed using graphs.},
 year = {2022}
}

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TY  - JOUR
T1  - Optimal Control Analysis of Meningococcal Meningitis Disease with Varying Population Size
AU  - Timothy Kiprono Yano
AU  - Jacob Bitok
AU  - Rael Jerop
Y1  - 2022/10/17
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N1  - https://doi.org/10.11648/j.acm.20221105.14
DO  - 10.11648/j.acm.20221105.14
T2  - Applied and Computational Mathematics
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JO  - Applied and Computational Mathematics
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PB  - Science Publishing Group
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AB  - Meningococcal meningitis is a fatal and scary highly infectious disease especially in the African meningitis disease belt and globally, its every community’s desire to wipe out meningitis disease by considering its prevention and control mechanisms. The paper formulates and analyzes a Meningococcal meningitis epidemic model that describes the spreading mechanisms of meningitis in a community with varying population. The stability analysis approach of non-linear systems is used to distinguish the properties of an epidemic deterministic compartmental model. The effective threshold reproductive value is determined by Jacobian approach and the stability study for the zero disease and endemic states are determined. Sensitivity indices analysis of the effective reproductive number to the crucial parameter values are established and rated accordingly. Using Pontryagin's approach to an optimal problem, the model was extended to include the following four control intervention measures: effort to prevent a disease infection by providing education needed, efforts to treat that minimizes sensitive and resistant strains and immunity control effort. The optimal control study of the applied control intervention efforts reveals that the use of prevention techniques and treatment efforts leads to a larger decrease of infections, thus becoming are the best intervention control strategy to eliminate the meningitis disease. Numerical analysis study was done for a combination of other strategies and main results are displayed using graphs.
VL  - 11
IS  - 5
ER  -

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Author Information

Timothy Kiprono Yano

Department of Mathematics and Computer Science, University of Eldoret, Eldoret, Kenya
Jacob Bitok

Department of Mathematics and Computer Science, University of Eldoret, Eldoret, Kenya
Rael Jerop

Department of Mathematics and Computer Science, University of Eldoret, Eldoret, Kenya

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Plain Text BibTeX RIS

APA Style

Timothy Kiprono Yano, Jacob Bitok, Rael Jerop. (2022). Optimal Control Analysis of Meningococcal Meningitis Disease with Varying Population Size. Applied and Computational Mathematics, 11(5), 140-149. https://doi.org/10.11648/j.acm.20221105.14

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ACS Style

Timothy Kiprono Yano; Jacob Bitok; Rael Jerop. Optimal Control Analysis of Meningococcal Meningitis Disease with Varying Population Size. Appl. Comput. Math. 2022, 11(5), 140-149. doi: 10.11648/j.acm.20221105.14

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AMA Style

Timothy Kiprono Yano, Jacob Bitok, Rael Jerop. Optimal Control Analysis of Meningococcal Meningitis Disease with Varying Population Size. Appl Comput Math. 2022;11(5):140-149. doi: 10.11648/j.acm.20221105.14

Copy | Download

@article{10.11648/j.acm.20221105.14,
  author = {Timothy Kiprono Yano and Jacob Bitok and Rael Jerop},
  title = {Optimal Control Analysis of Meningococcal Meningitis Disease with Varying Population Size},
  journal = {Applied and Computational Mathematics},
  volume = {11},
  number = {5},
  pages = {140-149},
  doi = {10.11648/j.acm.20221105.14},
  url = {https://doi.org/10.11648/j.acm.20221105.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20221105.14},
  abstract = {Meningococcal meningitis is a fatal and scary highly infectious disease especially in the African meningitis disease belt and globally, its every community’s desire to wipe out meningitis disease by considering its prevention and control mechanisms. The paper formulates and analyzes a Meningococcal meningitis epidemic model that describes the spreading mechanisms of meningitis in a community with varying population. The stability analysis approach of non-linear systems is used to distinguish the properties of an epidemic deterministic compartmental model. The effective threshold reproductive value is determined by Jacobian approach and the stability study for the zero disease and endemic states are determined. Sensitivity indices analysis of the effective reproductive number to the crucial parameter values are established and rated accordingly. Using Pontryagin's approach to an optimal problem, the model was extended to include the following four control intervention measures: effort to prevent a disease infection by providing education needed, efforts to treat that minimizes sensitive and resistant strains and immunity control effort. The optimal control study of the applied control intervention efforts reveals that the use of prevention techniques and treatment efforts leads to a larger decrease of infections, thus becoming are the best intervention control strategy to eliminate the meningitis disease. Numerical analysis study was done for a combination of other strategies and main results are displayed using graphs.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Optimal Control Analysis of Meningococcal Meningitis Disease with Varying Population Size
AU  - Timothy Kiprono Yano
AU  - Jacob Bitok
AU  - Rael Jerop
Y1  - 2022/10/17
PY  - 2022
N1  - https://doi.org/10.11648/j.acm.20221105.14
DO  - 10.11648/j.acm.20221105.14
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 140
EP  - 149
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20221105.14
AB  - Meningococcal meningitis is a fatal and scary highly infectious disease especially in the African meningitis disease belt and globally, its every community’s desire to wipe out meningitis disease by considering its prevention and control mechanisms. The paper formulates and analyzes a Meningococcal meningitis epidemic model that describes the spreading mechanisms of meningitis in a community with varying population. The stability analysis approach of non-linear systems is used to distinguish the properties of an epidemic deterministic compartmental model. The effective threshold reproductive value is determined by Jacobian approach and the stability study for the zero disease and endemic states are determined. Sensitivity indices analysis of the effective reproductive number to the crucial parameter values are established and rated accordingly. Using Pontryagin's approach to an optimal problem, the model was extended to include the following four control intervention measures: effort to prevent a disease infection by providing education needed, efforts to treat that minimizes sensitive and resistant strains and immunity control effort. The optimal control study of the applied control intervention efforts reveals that the use of prevention techniques and treatment efforts leads to a larger decrease of infections, thus becoming are the best intervention control strategy to eliminate the meningitis disease. Numerical analysis study was done for a combination of other strategies and main results are displayed using graphs.
VL  - 11
IS  - 5
ER  -

Copy | Download