Mathematics and Computing for Scientific Innovation Vol. 1

Malaria remains a major source of morbidity among children under five years of age in western Kenya, and the effectiveness of control measures depends on biological efficacy, adherence, vector behaviour, insecticide susceptibility, and local transmission conditions. This study develops a deterministic human–mosquito SIR–SI model for young children in a Bungoma County context and formulates five control measures representing effective vaccine protection, long-lasting insecticidal-net protection, treatment effort, larval-source management, and adult-vector removal. The model incorporates maturation out of the under-five population and assigns the vector-directed controls to biologically appropriate demographic processes. Positivity, boundedness, the effective reproduction number, disease-free stability, and local control sensitivity are analysed. A weighted Lyapunov function establishes global asymptotic stability of the disease-free equilibrium in the feasible region when the effective reproduction number is below one. A 100-day forward–backward sweep is used for structural scenario analysis rather than empirical calibration. The no-control scenario gives a basic reproduction number of 1.551, whereas the reference control profile yields an effective reproduction number of 0.292. Under the time-varying control solution, cumulative modelled incident infections decrease by 73.2% relative to no control, with lower integrated control effort than sustained high-intensity fixed-control scenarios. The results are model-based and should not be interpreted as current estimates of incidence, programme coverage, or economic cost-effectiveness in Bungoma County.