Asian Research Journal of Mathematics

Malaria remains an important cause of morbidity in young children in western Kenya, where intervention effectiveness depends not only on nominal coverage but also on biological efficacy, adherence, vector behaviour, insecticide susceptibility, and local transmission intensity. This study develops a deterministic human–mosquito model for children under five years of age and formulates a five-control optimal-control problem representing effective vaccine protection, long-lasting insecticidal-net protection, treatment effort, larval-source management, and adult-vector removal. The revised framework explicitly includes maturation out of the under-five population and assigns vector-control actions to biologically appropriate processes. The model is analysed for positivity, boundedness, the effective reproduction number, local and global stability of the disease-free equilibrium, and normalised control sensitivity. A weighted Lyapunov function establishes global asymptotic stability in the feasible region when the effective reproduction number is below unity. A 100-day forward–backward sweep simulation is then used as a structural scenario analysis rather than as an empirical calibration to Bungoma surveillance data. Under the no-control numerical scenario, the basic reproduction number is 1.551. A reference control profile reduces the effective reproduction number to 0.292. In the optimal-control simulation, cumulative modelled incident infections decline by 73.2% relative to the no-control trajectory while using substantially less integrated control effort than sustained high-intensity fixed-control scenarios. The results illustrate how intervention mechanisms, control effort, and terminal-time assumptions shape mathematical conclusions. They should not be interpreted as estimates of current Bungoma County incidence, programme coverage, or economic cost-effectiveness. The framework provides a transparent basis for future calibration with validated local surveillance, entomological, intervention-coverage, and cost data.