A Mathematical Model for Malaria Transmission Dynamics with Vaccination as a Control Variable in Children Under Five Years of Age

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.