TY  - JOUR
T1  - An optimal control strategy for cerebrospinal meningitis in Yobe State, Nigeria: a mathematical modeling approach
AU  - Shamaki, Timothy Ado
PY  - 2025
DA  - October
Y2  - 2025
DO  - 10.59292/bulletinbiomath.1724391
JF  - Bulletin of Biomathematics
JO  - Bull. Biomath.
PB  - Fırat Evirgen
WT  - DergiPark
SN  - 2980-1869
SP  - 192
EP  - 211
VL  - 3
IS  - 2
LA  - en
AB  - This paper develops and analyzes a deterministic SEIHR (Susceptible-Exposed-Infectious-Hospitalized-Recovered) model to investigate the transmission dynamics of cerebrospinal meningitis (CSM) and evaluate optimal control strategies. The framework incorporates three time-dependent control variables: mass vaccination of susceptible individuals, enhanced treatment for hospitalized patients, and public awareness campaigns. Using Pontryagin's Maximum Principle, we formulate an optimal control problem to minimize the number of infected individuals and the costs associated with the interventions. The basic reproduction number ($R_0$) is derived, and its sensitivity to key parameters is analyzed. Numerical simulations, using data relevant to the Yobe State context, demonstrate that a combined strategy of early, intensive vaccination, sustained treatment efforts, and effective public awareness is the most effective approach to mitigate the burden of a CSM outbreak. These findings provide quantitative support for evidence-based public health policies aimed at controlling meningitis in high-risk regions.
KW  - Cerebrospinal Meningitis
KW  - Mathematical Modeling
KW  - Optimal Control
KW  - Basic
Reproduction Number
KW  - Stability Analysis
CR  - [1] World Health Organization (WHO), Defeating Meningitis by 2030: A Global Road Map, (2021). https://www.who.int/publications/i/item/9789240026407
CR  - [2] Mount, H.R. and Boyle, S.D. Aseptic and bacterial meningitis: evaluation, treatment, and prevention. American Family Physician, 96(5), 314-322, (2017).
CR  - [3] Van de Beek, D., Cabellos, C., Dzupova, O., Esposito, S., Klein, M., Kloek, A.T. et al. ESCMID guideline: diagnosis and treatment of acute bacterial meningitis. Clinical Microbiology and Infection, 22, S37-S62, (2016).
CR  - [4] Fernandez, K., Lingani, C., Aderinola, O.M., Goumbi, K., Bicaba, B., Edea, Z.A. et al. Meningococcal meningitis outbreaks in the African meningitis belt after meningococcal serogroup A conjugate vaccine introduction, 2011–2017. The Journal of Infectious Diseases, 220(Supplement_4), S225-S232, (2019).
CR  - [5] Hasbun, R. (2022). Progress and challenges in bacterial meningitis: a review. Jama, 328(21), 2147-2154.
CR  - [6] Oordt-Speets, A.M., Bolijn, R., van Hoorn, R.C., Bhavsar, A. and Kyaw, M.H. Global etiology of bacterial meningitis: a systematic review and meta-analysis. PloS One, 13(6), e0198772, (2018).
CR  - [7] Premium Times, Meningitis Outbreak: Three dead, 30 Hospitalised in Gombe, (2025). https://www.premiumtimesng.com/regional/nnorth-east/784136-meningitis-outbreak-three-dead-30-hospitalised-in-gombe.html
CR  - [8] Nigeria Centre for Disease Control and Prevention, Weekly Epidemiological Report, Weekly updates on epidemics in Nigeria: as at 31st August 2025, (2025). https://ncdc.gov.ng/reports/weekly
CR  - [9] World Health Organization Nigeria, WHO Combats Cerebrospinal Meningitis Outbreak in Yobe State, Nigeria, (2024). https://www.afro.who.int/countries/nigeria/news/who-combats-cerebrospinal-meningitis-outbreak-yobe-state-nigeria
CR  - [10] Keeling, M.J. and Rohani, P. Modeling Infectious Diseases in Humans and Animals. Princeton University Press: New Jersey, (2008).
CR  - [11] Agusto, F.B. and Leite, M.C.A. Optimal control and cost-effective analysis of the 2017 meningitis outbreak in Nigeria. Infectious Disease Modelling, 4, 161-187, (2019).
CR  - [12] Crankson, M.V., Olotu, O., Afolabi, A.S. and Abidemi, A. Modeling the vaccination control of bacterial meningitis transmission dynamics: a case study. Mathematical Modelling and Control, 3(4), 416-434, (2023).
CR  - [13] Madaki, U.Y., Shu’aibu, A. and Umar, M.I. Mathematical model for the dynamics of bacterial meningitis (Meningococcal meningitis): a case study of Yobe State Specialist Hospital, Damaturu, Nigeria. Gadau Journal of Pure and Allied Sciences, 2(2), 113-129, (2023).
CR  - [14] Lenhart, S. and Workman, J.T. Optimal Control Applied to Biological Models. Chapman and Hall/CRC: New York, (2007).
CR  - [15] Van den Driessche, P. and Watmough, J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180(1-2), 29-48, (2002).
CR  - [16] Pontryagin, L.S. Mathematical Theory of Optimal Processes (Vol 4). CRC Press: London, (1987).
UR  - https://doi.org/10.59292/bulletinbiomath.1724391
L1  - https://dergipark.org.tr/en/download/article-file/4979230
ER  -