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A Mathematical Model for Malaria Transmission Dynamics with Vaccination as a Control Variable in Children Under Five Years of Age
Subject area: Science,Engineering and Technology · Area of research: Applied Mathematics
DOI: 10.64388/IREV9I11-1718271
Abstract
Malaria remains a major public health challenge for children under five years in sub-Saharan Africa. This paper develops an age structured SVIRSI compartmental model to simulate malaria transmission dynamics with RTS,S/AS01 vaccination as a control variable for children under five years in Bungoma County, Kenya. The model incorporates vaccination rate, vaccine efficacy, waning immunity, and mosquito control. The effective reproduction number R_e is derived via the next-generation matrix method. Positivity, boundedness, existence, uniqueness, local and global stability of the disease-free equilibrium are established. Sensitivity analysis identifies the most influential parameters. Bifurcation analysis reveals backward bifurcation. Numerical simulations using the fourth-order Runge-Kutta method confirm theoretical results. The computed R_e=0.00157<1 indicates that the current vaccination programme is sufficient for malaria elimination.
Keywords
Age Structured Model, Vaccine Efficacy, Vaccination, Effective Reproduction Number, Numerical Simulations
References
[1] C. Montoya and J.P. Romero-Leiton, Mathematical modelling for malaria under resistance and population movement, Revista Integración, temas de matemáticas, 38 (2020), 133–163. https://doi.org/10.18273/revint.v38n2-2020006
[2] P. Mukarugwiro and V. Nizeyimana, Simulation of mathematical modeling of malaria with vaccination, International Journal of Current Science Research and Review, 5 (2022), 4273–4282.
[3] P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 29–48. https://doi.org/10.1016/S0025-5564(02)00108-6
[4] M.A. Penny, R. Verity, C.A. Bever, C. Sauboin, K. Galactionova, S. Flasche, M.T. White, E.A. Wenger, N. Van de Velde, P. Pemberton-Ross, J.T. Griffin, T.A. Smith, P.A. Eckhoff, F. Muhib, M. Jit and A.C. Ghani, Public health impact and cost-effectiveness of the RTS,S/AS01 malaria vaccine: a systematic comparison of predictions from four mathematical models, The Lancet, 387 (10016) (2016), 367–375. https://doi.org/10.1016/S0140-6736(15)00725-4
[5] R. Resmawan and L. Yahya, Sensitivity analysis of mathematical model of Coronavirus Disease (COVID-19) transmission, CAUCHY, 6 (2020), 91–99. https://doi.org/10.18860/ca.v6i2.9165
[6] R. Resmawan and Nurwan, Konstruksi Bilangan Reproduksi pada Model Epidemik SEIRS-SEI Penyebaran Malaria dengan Vaksinasi dan Pengobatan, Jurnal Matematika Integratif, 13 (2) (2017), 105–114.
[7] D.L. Smith, J. Dushoff and F.E. McKenzie, The risk of a mosquito-borne infection in a heterogeneous environment, PLoS Biology, 2 (11) (2004), e368. https://doi.org/10.1371/journal.pbio.0020368
[8] C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications, Mathematical Biosciences and Engineering, 1 (2) (2004), 361–404. https://doi.org/10.3934/mbe.2004.1.361
[9] J.C. Butcher, Numerical Methods for Ordinary Differential Equations, 3rd ed., John Wiley & Sons, Chichester, 2016. https://doi.org/10.1002/9781119121534
How to cite this paper
@article{1718271,
author = {Opicho Dominic Simiyu, Bonface Kwach, Robert Nyukuri},
title = {A Mathematical Model for Malaria Transmission Dynamics with Vaccination as a Control Variable in Children Under Five Years of Age},
journal = {Iconic Research And Engineering Journals},
year = {2026},
volume = {9},
number = {11},
pages = {3456-3463},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1718271.pdf},
abstract = {Malaria remains a major public health challenge for children under five years in sub-Saharan Africa. This paper develops an age structured SVIRSI compartmental model to simulate malaria transmission dynamics with RTS,S/AS01 vaccination as a control variable for children under five years in Bungoma County, Kenya. The model incorporates vaccination rate, vaccine efficacy, waning immunity, and mosquito control. The effective reproduction number R_e is derived via the next-generation matrix method. Positivity, boundedness, existence, uniqueness, local and global stability of the disease-free equilibrium are established. Sensitivity analysis identifies the most influential parameters. Bifurcation analysis reveals backward bifurcation. Numerical simulations using the fourth-order Runge-Kutta method confirm theoretical results. The computed R_e=0.00157<1 indicates that the current vaccination programme is sufficient for malaria elimination.},
keywords = {Age Structured Model, Vaccine Efficacy, Vaccination, Effective Reproduction Number, Numerical Simulations},
month = {May},
doi = {https://doi.org/10.64388/IREV9I11-1718271}
}