ON THE MATHEMATICAL MODEL FOR THE SPREAD AND CONTROL OF MEASLES
DOI:
https://doi.org/10.33003/fjs-2025-0912-4301Keywords:
Vaccination, Treatment, Disease-Free Equilibrium, MeV (Measles Virus), InfectionAbstract
Measles is a highly contagious and potentially deadly disease that continues to pose a significant public health challenge, particularly in regions with suboptimal vaccination coverage. Measles remains a major threat to children, leading to severe complications and even death, despite the success of vaccination programs worldwide. This study delves into the dynamics of measles transmission and control, focusing on the development of a mathematical model. The research aims to propose a mathematical model using a system of first-order differential equations, categorizing the population into compartments representing vaccination(V), susceptible(S), exposed(E), infection(I), treatment(T) and recovery(R). The objectives include: obtaining Disease-Free Equilibrium State (DFES), performing stability analysis for DFES and the numerical simulation of the model was presented using maple software. Ultimately, the goal is to inform evidence-based strategies for measles vaccination and prevention, mitigating the disease's impact on children's health.
References
Christopher, O., Ibrahim, I. A., & Shamaki, T. A. (2017). Mathematical Model for the Dynamics of Measles under the Combined Effect of Vaccination and Measles Therapy, International Journal of Science and Technology (IJST) – Volume 6 No.6, June, 2017.
Centers for Disease Control and Prevention. (2025). Chapter 7: Measles — Manual for the Surveillance of Vaccine-Preventable Diseases. https://www.cdc.gov/surv-manual/php/table-of-contents/chapter-7-measles.htm
Centers for Disease Control and Prevention. (2024). Chapter 13: Measles — Pink Book. https://www.cdc.gov/pinkbook/hcp/table-of-contents/chapter-13-measles.html
Federal Reserve Bank of St. Louis. (2025). Crude Birth Rate for Nigeria [SPDYNCBRTINNGA]. https://fred.stlouisfed.org/series/SPDYNCBRTINNGA
Guerra, F. M., Bolotin, S., Lim, G., Heffernan, J. M., Deeks, S. L., Li, Y., & Crowcroft, N. S. (2017). The basic reproduction number (R0) of measles: A systematic review. The Lancet Infectious Diseases, 17(12), e420–e428. https://www.sciencedirect.com/science/article/pii/S1473309917303079
He, J. H., (2000). A coupling method of a homotopy technique and a perturbation technique for non-linear problems. Int. J. Non-Linear Mech., 351: 37- 43.
Kolawole, M. K., & Akin-Awoniran, B. O. (2025). The impact of multifaceted vaccination interventions on measles eradication: A behavioral analysis of the SEITRV epidemic
model. FUDMA Journal of Sciences, 9(11). https://doi.org/10.33003/fjs-2025-0911-3740
Kouadio, I. K., Kamigaki, T., & Oshitani, H. (2010). Measles outbreaks in displaced populations: a review of transmission, morbidity and mortality associated factors. International Health and Human Rights, 10(1), 5.
https://doi.org/10.1186/1472-698X-10-5
Madubueze, C. E., Onwubuya, I. O., & Mzungwega, I. (2022). Controlling Measles Transmission Dynamics with Optimal Control Analysis, Ratio Mathematica Volume 43, 2022.
Mahmoud, A. I., & Attila, D. (2023). Stability and Threshold Dynamics in a Seasonal Mathematical Model for Measles Outbreaks with Double-Dose Vaccination, Mathematics 2023, 11, 1791.
Momoh, A. A., Ibrahim, M. O., Uwanta, I. J., & Manga, S. B. (2013). Mathematical Model for Control of Measles Epidemiology, International Journal of Pure and Applied Mathematics, Volume 87 No. 5, 2013, 707-718.
Ochi, P. O., Agada, A. A., Nworah, I. B., Nworah, D. A., & Goni, A. N. (2024). Local and global stability analysis of measles epidemic model at disease-free equilibrium. FUDMA Journal of Sciences, 8(1), 369 – 379. https://doi.org/10.33003/fjs-2024-0801-2219
Portnoy, A., Jit, M., Ferrari, M., Hanson, M., Brenzel, L., & Verguet, S. (2019). Estimates of case-fatality ratios of measles in low-income and middle-income countries: A systematic review and modelling analysis. The Lancet Global Health, 7(4), e472–e481. https://www.thelancet.com/journals/langlo/article/PIIS2214-109X(18)30537-0/fulltext
Prem, K., Cook, A. R., & Jit, M. (2017). Projecting social contact matrices in 152 countries using contact surveys and demographic data. PLOS Computational Biology, 13(9), e1005697. https://doi.org/10.1371/journal.pcbi.1005697
Samuel, O. S., Abdullahi, I., Daouda, S., & Ahmed, O. L. (2020). Mathematical model for measles disease with control on the susceptible and exposed compartments, Open Journal of Mathematical Analysis 2020, 4(1), 60-75.
Stephen, E., Kitengeso, R. E., Kiria, G. T., Felician, N., Mwema, G. G., & Mafarasa, A. P. (2015). A Mathematical Model for Control and Elimination of the Transmission Dynamics of Measles, Applied and Computational Mathematics, 4(6), 2015, pp. 396-
408.
World Bank. (2025). Death rate, crude (per 1,000 people) — Nigeria (SP.DYN.CDRT.IN). https://data.worldbank.org/indicator/SP.DYN.CDRT.IN?locations=NG
World Health Organization, & United Nations Children’s Fund. (2023). Nigeria — WHO/UNICEF estimates of immunization coverage (WUENIC) country profile, 2023 [PDF]. https://cdn.who.int/media/docs/default-source/country-profiles/immunization/2023-country-profiles/immunization_nga_2023.pdf
World Health Organization. (2013). Pocket book of hospital care for children: Guidelines for the management of common childhood illnesses (2nd ed.). World Health Organization. https://www.who.int/publications/i/item/978-92-4-154837-3
World Health Organization. (2017). Measles vaccines: WHO position paper – April 2017. Weekly Epidemiological Record, 92(17), 205–227. https://www.who.int/teams/immunization-vaccines-and-biologicals/policies/position-papers/measles
World Health Organization (WHO 2024) on Measles for children, World Health Organization - History of Measles Vaccine.
World Health Organization. (2025). On measles for children, Measles Treatment for Child.
Downloads
Published
Issue
Section
Categories
License
Copyright (c) 2025 Sule Santali Santali, Bawa Musa, Agboluaje Ayodele Abraham, Abdulkadir Abubakar
This work is licensed under a Creative Commons Attribution 4.0 International License.
