In this paper, the analysis of a mathematical model for the control of measles using vaccination is presented. The disease reproductive number (R0) is computed and used to derive an expression of a reduction factor in the disease spread resulting from the implementation of immunization program in the community. The Routh-Hurwitz stability conditions are adopted to analyze the model equilibria in terms of their local stability. Lyapunov function candidates are used to determine the global stability status of both the measles-free and measles-persistent equilibrium states. Elasticity index of each parameter embedded into is computed to help ascertain the significance of the model parameter contribution to measles epidemics in the society. Furthermore, population simulations are performed to demonstrate how changes in some parameter values influence the dynamical evolution of our model population sub-classes.
Cite this paper
Konlan, M. , Gunu, R. I. M. and Iddrisu, A. (2026). Mathematical Modelling and Analysis of Measles Control Using Vaccination. Open Access Library Journal, 13, e15019. doi: http://dx.doi.org/10.4236/oalib.1115019.
Nigusie Mitku, S. and Koya, P.R. (2017) Mathematical Modeling and Simulation Study for the Control and Transmission Dynamics of Measles. American Journal of Applied Mathematics, 5, 99-107. https://doi.org/10.11648/j.ajam.20170504.11
Peter, O.J., Panigoro, H.S., Ibrahim, M.A., Otunuga, O.M., Ayoola, T.A. and Oladapo, A.O. (2023) Analysis and Dynamics of Measles with Control Strategies: A Mathematical Modeling Approach. International Journal of Dynamics and Control, 11, 2538-2552. https://doi.org/10.1007/s40435-022-01105-1
Opoku, S., Seidu, B. and Akuka, P.N.A. (2023) A Mathematical Analysis of the Impact of Maternally Derived Immunity and Double-Dose Vaccination on the Spread and Control of Measles. Computational and Mathematical Biophysics, 11, Article ID: 20230106. https://doi.org/10.1515/cmb-2023-0106
Garba, S.M., Safi, M.A. and Usaini, S. (2017) Mathematical Model for Assessing the Impact of Vaccination and Treatment on Measles Transmission Dynamics. Mathematical Methods in the Applied Sciences, 40, 6371-6388. https://doi.org/10.1002/mma.4462
James Peter, O., Ojo, M.M., Viriya-pong, R. and Abiodun Oguntolu, F. (2022) Mathematical Model of Measles Transmission Dynamics Using Real Data from Nigeria. Journal of Difference Equations and Applications, 28, 753-770. https://doi.org/10.1080/10236198.2022.2079411
Arsal, S.R., Aldila, D. and Handari, B.D. (2020) Short Review of Mathematical Model of Measles. AIP Conference Proceedings, 2264, Article 020003. https://doi.org/10.1063/5.0023439
Edward, S., Raymond, K.E., Gabriel, K.T., Nestory, F., Godfrey, M.G. and Arbogast, M.P. (2015) A Mathematical Model for Control and Elimination of the Transmission Dynamics of Measles. Applied and Computational Mathematics, 4, 396-408. https://doi.org/10.11648/j.acm.20150406.12
Jaharuddin and Bakhtiar, T. (2020) Control Policy Mix in Measles Transmission Dynamics Using Vaccina-tion, Therapy, and Treatment. International Journal of Mathematics and Mathematical Sciences, 2020, Article ID: 1561569. https://doi.org/10.1155/2020/1561569
Wang, R., Jing, W., Liu, M. and Liu, J. (2022) Trends of the Global, Regional, and National Incidence of Measles, Vaccine Coverage, and Risk Factors in 204 Countries from 1990 to 2019. Fron-tiers in Medicine, 8, Article ID: 798031. https://doi.org/10.3389/fmed.2021.798031
Rahmayani, S.A., Aldila, D. and Handari, B.D. (2021) Cost-Effectiveness Analysis on Measles Transmission with Vaccination and Treatment Intervention. AIMS Mathematics, 6, 12491-12527. https://doi.org/10.3934/math.2021721
Konlan, M., Abassawah Danquah, B., Okyere, E., Osman, S., Amenyo Kessie, J. and Kobina Donkoh, E. (2024) Global Stability Analysis and Modelling Onchocerciasis Transmission Dynamics with Control Measures. Infection Ecology & Epidemiology, 14, Article 2347941. https://doi.org/10.1080/20008686.2024.2347941
Konlan, M. (2024) Modeling the Inflow of Exposed and Infected Migrants on the Dynamics of Ma-laria. European Journal of Mathematical Analysis, 4, Article 7. https://doi.org/10.28924/ada/ma.4.7
Wireko, F.A., Asamoah, J.K.K., Adu, I.K. and Ndogum, S. (2024) Non-Optimal and Optimal Fractional Control Analysis of Measles Using Real Data. Informatics in Medicine Unlocked, 49, Ar-ticle 101548. https://doi.org/10.1016/j.imu.2024.101548
Kuddus, M.A., Mohiuddin, M. and Rahman, A. (2021) Mathematical Analysis of a Measles Transmission Dy-namics Model in Bangladesh with Double Dose Vaccination. Scientific Reports, 11, Article No. 16571. https://doi.org/10.1038/s41598-021-95913-8
Memon, Z., Qureshi, S. and Memon, B.R. (2020) Mathematical Analysis for a New Nonlinear Measles Epidemiological System Using Real Incidence Data from Pakistan. The European Physical Journal Plus, 135, Article No. 378. https://doi.org/10.1140/epjp/s13360-020-00392-x
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Ojo, M.M. and Goufo, E.F.D. (2021) Assessing the Impact of Control Interventions and Awareness on Ma-laria: A Mathematical Modeling Approach. Communications in Mathematical Bi-ology and Neuroscience, 2021, Article ID: 93.
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