Computational Modelling of Two Strain Meningitis Disease Outbreak

Timothy Kiprono Yano; Jacob Bitok

doi:doi:10.11648/j.acm.20221105.12

| Peer-Reviewed

Computational Modelling of Two Strain Meningitis Disease Outbreak

Timothy Kiprono Yano, Jacob Bitok

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

Received: 11 September 2022 Accepted: 26 September 2022 Published: 11 October 2022

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

Meningococcal meningitis is a significant contributor to increased deaths globally, particularly the vulnerable children aged between 0-5 years. This paper formulates a robust two-strain epidemic model for the transmission dynamics of bacterial meningitis by incorporating interventions such as treatment and vaccination. The aim of the article is to formulate a meningitis epidemic model and study the time dependent dynamics of meningitis in the presence of antibiotic resistance to treatment threats while assessing the impact of vaccination proportion. The study uses the 4^th order Runge Kutta numerical approach to solve the problem and Maple mathematical tool to undertake simulations. The meningitis model qualitative study reveals existence of disease-free state when infection dies out and endemic state when disease persist in the community. The disease-free case is found to be stable only if effective reproduction number Re < 1 and the community enjoys disease free scenario. Meningitis disease-free state reveals a locally asymptotically stable (LAS) transmission dynamics. The endemic equilibrium state i.e., Re > 1 exists and persistence occurs in the community. The impact of parameter control measures on the spread of meningitis disease through sensitivity study of the key parameter, i.e., Re, which revealed the key target parameters that can wipe out meningitis disease. We perform numerical solution of the considered model equations to display the qualitative findings and describe the asymptotical transmission dynamics of the disease. The effects of meningitis disease prevention and control approaches are analyzed. Key findings are shown using graphs and tables. We obtain a threshold vaccination proportion value beyond which the meningitis disease will be perfectly wiped out of the community and below which the disease acquires endemic state.

Published in	Applied and Computational Mathematics (Volume 11, Issue 5)
DOI	10.11648/j.acm.20221105.12
Page(s)	123-129
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, Vaccination Coverage, Endemic Equilibrium, Sensitivity Indices, Numerical Simulation

References

[1]	Asamoah, J. K. K., Nyabadza, F., Seidu, B., Chand, M., & Dutta, H. (2018). Mathematical modelling of bacterial meningitis transmission dynamics with control measures. Computational and mathematical methods in medicine, 2018.
[2]	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.
[3]	Boyce, W. E., DiPrima, R. C., & Haines, C. W. (2001). Elementary differential equations and boundary value problems, volume 9. Wiley New York.
[4]	Christodoulou, N. S. (2009). An algorithm using Runge-Kutta methods of orders 4 and 5 for systems of odes. Int. J. Numer. Methods Appl, 2 (1), 47-57.
[5]	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.
[6]	Martínez, M. F., Merino, E. G., Sánchez, E. G., Sánchez, J. G., del Rey, A. M., & Sánchez, G. R. (2013). A mathematical model to study the meningococcal meningitis. Procedia Computer Science, 18, 2492-2495.
[7]	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.
[8]	Mbaeyi Sarah, Jonathan Duffy, M. L. A. (2020). Meningococcal disease. CDC Reports.
[9]	Organization, W. H. et al. (2007). Standardized treatment of bacterial meningitis in Africa in epidemic and non-epidemic situations. Technical report, World Health Organization.
[10]	Tilahun, G. T. (2019). Optimal control analysis of pneumonia and meningitis coinfection. Computational and Mathematical Methods in Medicine, 2019.
[11]	Vereen, K. (2008). An scir model of meningococcal meningitis.
[12]	Yano, K. T. (2018). SEIR Childhood Disease Model with Constant Vaccination Strategy. PhD thesis, JKUAT-PAUSTI.
[13]	Afolabi, M. A., Adewoye, K. S., Folorunso, A. I., & Omoloye, M. A. (2021). A mathematical model on transmission dynamics of meningococcal meningitis. Iconic Research and Engineering Journal, (pp. 59–66).
[14]	Agusto, F. & Leite, M. (2019). Optimal control and cost-effective analysis of the 2017 meningitis outbreak in Nigeria. Infectious Disease Modelling, 4, 161–187.
[15]	Pinkert, J. R. (1976). An exact method for finding the roots of a complex polynomial. ACM Transactions on Mathematical Software (TOMS), 2 (4), 351–363.
[16]	Marsden, J. E., Sirovich, L., Antman, S. S., Iooss, G., Holmes, P., Barkley, D., & Newton, P. Texts in Applied Mathematics 37.

Cite This Article

Plain Text BibTeX RIS

APA Style

Timothy Kiprono Yano, Jacob Bitok. (2022). Computational Modelling of Two Strain Meningitis Disease Outbreak. Applied and Computational Mathematics, 11(5), 123-129. https://doi.org/10.11648/j.acm.20221105.12

Copy | Download

ACS Style

Timothy Kiprono Yano; Jacob Bitok. Computational Modelling of Two Strain Meningitis Disease Outbreak. Appl. Comput. Math. 2022, 11(5), 123-129. doi: 10.11648/j.acm.20221105.12

Copy | Download

AMA Style

Timothy Kiprono Yano, Jacob Bitok. Computational Modelling of Two Strain Meningitis Disease Outbreak. Appl Comput Math. 2022;11(5):123-129. doi: 10.11648/j.acm.20221105.12

Copy | Download

@article{10.11648/j.acm.20221105.12,
  author = {Timothy Kiprono Yano and Jacob Bitok},
  title = {Computational Modelling of Two Strain Meningitis Disease Outbreak},
  journal = {Applied and Computational Mathematics},
  volume = {11},
  number = {5},
  pages = {123-129},
  doi = {10.11648/j.acm.20221105.12},
  url = {https://doi.org/10.11648/j.acm.20221105.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20221105.12},
  abstract = {Meningococcal meningitis is a significant contributor to increased deaths globally, particularly the vulnerable children aged between 0-5 years. This paper formulates a robust two-strain epidemic model for the transmission dynamics of bacterial meningitis by incorporating interventions such as treatment and vaccination. The aim of the article is to formulate a meningitis epidemic model and study the time dependent dynamics of meningitis in the presence of antibiotic resistance to treatment threats while assessing the impact of vaccination proportion. The study uses the 4th order Runge Kutta numerical approach to solve the problem and Maple mathematical tool to undertake simulations. The meningitis model qualitative study reveals existence of disease-free state when infection dies out and endemic state when disease persist in the community. The disease-free case is found to be stable only if effective reproduction number Re Re > 1 exists and persistence occurs in the community. The impact of parameter control measures on the spread of meningitis disease through sensitivity study of the key parameter, i.e., Re, which revealed the key target parameters that can wipe out meningitis disease. We perform numerical solution of the considered model equations to display the qualitative findings and describe the asymptotical transmission dynamics of the disease. The effects of meningitis disease prevention and control approaches are analyzed. Key findings are shown using graphs and tables. We obtain a threshold vaccination proportion value beyond which the meningitis disease will be perfectly wiped out of the community and below which the disease acquires endemic state.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Computational Modelling of Two Strain Meningitis Disease Outbreak
AU  - Timothy Kiprono Yano
AU  - Jacob Bitok
Y1  - 2022/10/11
PY  - 2022
N1  - https://doi.org/10.11648/j.acm.20221105.12
DO  - 10.11648/j.acm.20221105.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 123
EP  - 129
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20221105.12
AB  - Meningococcal meningitis is a significant contributor to increased deaths globally, particularly the vulnerable children aged between 0-5 years. This paper formulates a robust two-strain epidemic model for the transmission dynamics of bacterial meningitis by incorporating interventions such as treatment and vaccination. The aim of the article is to formulate a meningitis epidemic model and study the time dependent dynamics of meningitis in the presence of antibiotic resistance to treatment threats while assessing the impact of vaccination proportion. The study uses the 4th order Runge Kutta numerical approach to solve the problem and Maple mathematical tool to undertake simulations. The meningitis model qualitative study reveals existence of disease-free state when infection dies out and endemic state when disease persist in the community. The disease-free case is found to be stable only if effective reproduction number Re Re > 1 exists and persistence occurs in the community. The impact of parameter control measures on the spread of meningitis disease through sensitivity study of the key parameter, i.e., Re, which revealed the key target parameters that can wipe out meningitis disease. We perform numerical solution of the considered model equations to display the qualitative findings and describe the asymptotical transmission dynamics of the disease. The effects of meningitis disease prevention and control approaches are analyzed. Key findings are shown using graphs and tables. We obtain a threshold vaccination proportion value beyond which the meningitis disease will be perfectly wiped out of the community and below which the disease acquires endemic state.
VL  - 11
IS  - 5
ER  -

Copy | Download

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

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Timothy Kiprono Yano, Jacob Bitok. (2022). Computational Modelling of Two Strain Meningitis Disease Outbreak. Applied and Computational Mathematics, 11(5), 123-129. https://doi.org/10.11648/j.acm.20221105.12

Copy | Download

ACS Style

Timothy Kiprono Yano; Jacob Bitok. Computational Modelling of Two Strain Meningitis Disease Outbreak. Appl. Comput. Math. 2022, 11(5), 123-129. doi: 10.11648/j.acm.20221105.12

Copy | Download

AMA Style

Timothy Kiprono Yano, Jacob Bitok. Computational Modelling of Two Strain Meningitis Disease Outbreak. Appl Comput Math. 2022;11(5):123-129. doi: 10.11648/j.acm.20221105.12

Copy | Download

@article{10.11648/j.acm.20221105.12,
  author = {Timothy Kiprono Yano and Jacob Bitok},
  title = {Computational Modelling of Two Strain Meningitis Disease Outbreak},
  journal = {Applied and Computational Mathematics},
  volume = {11},
  number = {5},
  pages = {123-129},
  doi = {10.11648/j.acm.20221105.12},
  url = {https://doi.org/10.11648/j.acm.20221105.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20221105.12},
  abstract = {Meningococcal meningitis is a significant contributor to increased deaths globally, particularly the vulnerable children aged between 0-5 years. This paper formulates a robust two-strain epidemic model for the transmission dynamics of bacterial meningitis by incorporating interventions such as treatment and vaccination. The aim of the article is to formulate a meningitis epidemic model and study the time dependent dynamics of meningitis in the presence of antibiotic resistance to treatment threats while assessing the impact of vaccination proportion. The study uses the 4th order Runge Kutta numerical approach to solve the problem and Maple mathematical tool to undertake simulations. The meningitis model qualitative study reveals existence of disease-free state when infection dies out and endemic state when disease persist in the community. The disease-free case is found to be stable only if effective reproduction number Re Re > 1 exists and persistence occurs in the community. The impact of parameter control measures on the spread of meningitis disease through sensitivity study of the key parameter, i.e., Re, which revealed the key target parameters that can wipe out meningitis disease. We perform numerical solution of the considered model equations to display the qualitative findings and describe the asymptotical transmission dynamics of the disease. The effects of meningitis disease prevention and control approaches are analyzed. Key findings are shown using graphs and tables. We obtain a threshold vaccination proportion value beyond which the meningitis disease will be perfectly wiped out of the community and below which the disease acquires endemic state.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Computational Modelling of Two Strain Meningitis Disease Outbreak
AU  - Timothy Kiprono Yano
AU  - Jacob Bitok
Y1  - 2022/10/11
PY  - 2022
N1  - https://doi.org/10.11648/j.acm.20221105.12
DO  - 10.11648/j.acm.20221105.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 123
EP  - 129
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20221105.12
AB  - Meningococcal meningitis is a significant contributor to increased deaths globally, particularly the vulnerable children aged between 0-5 years. This paper formulates a robust two-strain epidemic model for the transmission dynamics of bacterial meningitis by incorporating interventions such as treatment and vaccination. The aim of the article is to formulate a meningitis epidemic model and study the time dependent dynamics of meningitis in the presence of antibiotic resistance to treatment threats while assessing the impact of vaccination proportion. The study uses the 4th order Runge Kutta numerical approach to solve the problem and Maple mathematical tool to undertake simulations. The meningitis model qualitative study reveals existence of disease-free state when infection dies out and endemic state when disease persist in the community. The disease-free case is found to be stable only if effective reproduction number Re Re > 1 exists and persistence occurs in the community. The impact of parameter control measures on the spread of meningitis disease through sensitivity study of the key parameter, i.e., Re, which revealed the key target parameters that can wipe out meningitis disease. We perform numerical solution of the considered model equations to display the qualitative findings and describe the asymptotical transmission dynamics of the disease. The effects of meningitis disease prevention and control approaches are analyzed. Key findings are shown using graphs and tables. We obtain a threshold vaccination proportion value beyond which the meningitis disease will be perfectly wiped out of the community and below which the disease acquires endemic state.
VL  - 11
IS  - 5
ER  -

Copy | Download