Home / Current Issue / Paper 1718271
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: https://doi.org/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
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}
}