A Diffusion-Reaction Model for the Spread and Control of an Infectious Disease: A Case Study of Meningitis Outbreak in Zamfara State, Nigeria
Keywords:
Infectious diseases, Diffusion-reaction, Finite difference, method, Meningitis, Data-driven approach
Abstract
Infectious diseases abound in the world, affecting and even claiming the lives of many of their victims. Many researches have been conducted with the goal of proffering how to curtail or control the spread of the diseases. A diffusion-reaction model is herein proposed for the spread and control of an infectious disease. A numerical approach is considered for the solution of the proposed model. With the aid of data generated from an instance of meningitis outbreak, the rate of spread of the disease and the quantity of treatment, to apply to control the disease, are determined.
References
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Njidda, A., Raji, I., Lawal, S., Yusuff, H., Aniaku, E., Usman, R., ... Nguku, P. (2021). Descriptive characterization of the cerebrospinal meningitis outbreak in Zamfara State, 2017-18. Journal of Interventional Epidemiology and Public Health, 4, Article 19. https://doi.org/10.11604/ijeph.2021.4.19
Yahaya A. M. & Aliyu I. I. (2019) Knowledge, Attitudes and Practices Towards Type C Meningitis: A Qualitative Study in Zamfara State, Nigeria. Lapai Journal of Politics 5, 3
Crank, J. & Nilcson, P. (1947) A Practical Method for Numerical Evaluation of Solutions of Partial Differential Equations of the Heat Conduction Type. Proc. Camb. Phil. Soc. 43, 50-67.
Kwambana-Adams B. A., Rahab C. A., Catherine O., Murtala R., Archibald W., Ebenezer F. N., Bernard E., Abdul K. S., Madikay S., Abdullahi S. U., Rabi U., Adamu A., Garba A., Yahaya B., Rabiu S., Husaini U. B., Bashir A., Alliyu I. Y., Badaru S., Aderinola O. M., Popoola M. O., Ekeng E., Adebola O., Nwando M., Adamu K., Ibrahim N. M., Okudo I., Stephen M., Olivier R., Jason B., Jason M. M., Mohammed A., Sulaiman A. G., Adebayo A., Andre B., Linda O., Mamoutou H. D., Wondimagegnehu A., Umberto D'A., Chikwe I. & Martin A. (2018) Meningococcus serogroup C Clonal Complex ST-10217 Outbreak in Zamfara State, Northern Nigeria Scientific Reports DOI:10.1038/s41598-018-32475-2
Obaro, S. K. & Habib A. G. (2016) Control of Meningitis Outbreaks In The African Meningitis Belt, Lancet, 16(4), 400-402. Pubmed PMID: 27036337.
Trotter, C. L., Lingani, C., Fernandez K., Cooper, L. V., Bita, A., Tevi-Benissan, C., Ronveaux, O., Preziosi, M., Stuart, J. M. (2017) Impact of MenAfriVac in nine countries of the African meningitis belt, 2010-2015. The Lancet Healthy Longevity 17(8), 867-872 DOI:https://doi.org/10.1016/S1473-3099(17)30301-8
Karimi, K. J. M., Rotich, T., & Kaneba, C.(2025). Mathematical Model for Ions Transport Optimization in an Animal Cell Using MATLAB. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 11(2):62-73
Bello, J. F., Taiwo E. S., & Adinya, I.(2024). Modified Models for Constrained Means Absolute Deviation Portfolio Optimization. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 10(1):12-24
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Monteil, C. L., Jolley, K. A., Bronsvoort, B. M., McIntyre, M. C., Remé, T., Viguie, C., ... Maiden, M. C. (2018). Meningococcus serogroup C Clonal Complex ST-10217 outbreak in Zamfara State, Northern Nigeria. Emerging Infectious Diseases, 24(1), 87-94. https://doi.org/10.3201/eid2401.171586
Centers for Disease Control and Prevention (2018) Bacterial Meningitis. Atlanta https://www.cdc.gov/meningitis/bacterial.html
Centers for Disease Control and Prevention (2018) Atlanta Chapter 2: Epidemiology of meningitis caused by Neisseria meningitidis, Streptococcus pneumoniae, and Haemophilus influenza. https://www.cdc.gov/meningitis/lab-manual/chpt02-epi.html.
Juan L. V. (2017) The mathematical theories of diffusion, Nonlinear and fractional diffusion. Universidad Autonoma de Madrid, Spain.
Smith G. D. (1978) Numerical Solution of Partial Differential Equations, Oxford University Press, Oxford.
World Health Organization (2025) WHO guidelines on meningitis diagnosis, treatment and care. Geneva: World Health Organization Licence: CC BY-NC-SA 3.0 IGO.
Benington-Castro J. (2018) Bacterial Meningitis: Types, Systems, Causes and Treatment. Everyday Health, 1298-1307.
Andrew J. & Manish S. (2016) Neisseria meningitidis(Meningococcus) in.: Nelson Textbook of Paediatrics. Elsevier, 1357-1365.
WHO Regional Office. (2009) Standard Operating Procedures For Enhanced Meningitis Surveillance. Geneva, Switzerland.
World Health Organization. (2023). Meningitis in Africa: Factsheet and country risk maps.
Federal Ministry of Health (2013) Integrated Disease Surveillance and Response Technical Guidelines. 346-347.
Daniel, D. (2025, April), Zamfara 90% ready for future meningitis outbreak. Daily Trust.
Njidda, A., Raji, I., Lawal, S., Yusuff, H., Aniaku, E., Usman, R., ... Nguku, P. (2021). Descriptive characterization of the cerebrospinal meningitis outbreak in Zamfara State, 2017-18. Journal of Interventional Epidemiology and Public Health, 4, Article 19. https://doi.org/10.11604/ijeph.2021.4.19
Yahaya A. M. & Aliyu I. I. (2019) Knowledge, Attitudes and Practices Towards Type C Meningitis: A Qualitative Study in Zamfara State, Nigeria. Lapai Journal of Politics 5, 3
Crank, J. & Nilcson, P. (1947) A Practical Method for Numerical Evaluation of Solutions of Partial Differential Equations of the Heat Conduction Type. Proc. Camb. Phil. Soc. 43, 50-67.
Kwambana-Adams B. A., Rahab C. A., Catherine O., Murtala R., Archibald W., Ebenezer F. N., Bernard E., Abdul K. S., Madikay S., Abdullahi S. U., Rabi U., Adamu A., Garba A., Yahaya B., Rabiu S., Husaini U. B., Bashir A., Alliyu I. Y., Badaru S., Aderinola O. M., Popoola M. O., Ekeng E., Adebola O., Nwando M., Adamu K., Ibrahim N. M., Okudo I., Stephen M., Olivier R., Jason B., Jason M. M., Mohammed A., Sulaiman A. G., Adebayo A., Andre B., Linda O., Mamoutou H. D., Wondimagegnehu A., Umberto D'A., Chikwe I. & Martin A. (2018) Meningococcus serogroup C Clonal Complex ST-10217 Outbreak in Zamfara State, Northern Nigeria Scientific Reports DOI:10.1038/s41598-018-32475-2
Obaro, S. K. & Habib A. G. (2016) Control of Meningitis Outbreaks In The African Meningitis Belt, Lancet, 16(4), 400-402. Pubmed PMID: 27036337.
Trotter, C. L., Lingani, C., Fernandez K., Cooper, L. V., Bita, A., Tevi-Benissan, C., Ronveaux, O., Preziosi, M., Stuart, J. M. (2017) Impact of MenAfriVac in nine countries of the African meningitis belt, 2010-2015. The Lancet Healthy Longevity 17(8), 867-872 DOI:https://doi.org/10.1016/S1473-3099(17)30301-8
Karimi, K. J. M., Rotich, T., & Kaneba, C.(2025). Mathematical Model for Ions Transport Optimization in an Animal Cell Using MATLAB. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 11(2):62-73
Bello, J. F., Taiwo E. S., & Adinya, I.(2024). Modified Models for Constrained Means Absolute Deviation Portfolio Optimization. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 10(1):12-24
Elflein John (2021), www.statista.com/statistics/1105235/coronavirus-2019ncov-cases-recoveries-daths-most-affected-countries-worldwide/
Monteil, C. L., Jolley, K. A., Bronsvoort, B. M., McIntyre, M. C., Remé, T., Viguie, C., ... Maiden, M. C. (2018). Meningococcus serogroup C Clonal Complex ST-10217 outbreak in Zamfara State, Northern Nigeria. Emerging Infectious Diseases, 24(1), 87-94. https://doi.org/10.3201/eid2401.171586
Centers for Disease Control and Prevention (2018) Bacterial Meningitis. Atlanta https://www.cdc.gov/meningitis/bacterial.html
Centers for Disease Control and Prevention (2018) Atlanta Chapter 2: Epidemiology of meningitis caused by Neisseria meningitidis, Streptococcus pneumoniae, and Haemophilus influenza. https://www.cdc.gov/meningitis/lab-manual/chpt02-epi.html.
Juan L. V. (2017) The mathematical theories of diffusion, Nonlinear and fractional diffusion. Universidad Autonoma de Madrid, Spain.
Smith G. D. (1978) Numerical Solution of Partial Differential Equations, Oxford University Press, Oxford.
Published
2025-12-10
How to Cite
Akindoyin, M., Bamigbola, O., & Onanaye, A. (2025). A Diffusion-Reaction Model for the Spread and Control of an Infectious Disease: A Case Study of Meningitis Outbreak in Zamfara State, Nigeria. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 11(4), 35 - 45. Retrieved from https://ijmso.unilag.edu.ng/article/view/2913
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