Analytical Study of Optimal Control Strategies for Malaria Transmission Dynamics in Kano State

This study formulates and analyses optimal control strategies for malaria transmission dynamics in Kano State, North West Nigeria, using a deterministic compartmental epidemiological model that incorporates both human and mosquito population dynamics. Kano State reports among the highest malaria burdens in Nigeria, with the disease accounting for a substantial proportion of under-five mortality and outpatient morbidity in public health facilities. A susceptible-exposed-infectious-recovered-susceptible model for the human population is coupled with a susceptible-exposed-infectious model for the Anopheles mosquito vector, incorporating temperature-dependent mosquito development rates calibrated to Kano's seasonal climate. Three control interventions, namely insecticide-treated bednet distribution, indoor residual spraying, and artemisinin-based combination therapy coverage, are incorporated as time-varying control functions within the optimal control framework. Pontryagin's maximum principle is applied to derive the optimality conditions, and the resulting two-point boundary value problem is solved numerically using the forward-backward sweep algorithm. Cost-effectiveness analysis using incremental cost-effectiveness ratios is applied to rank single and combined intervention strategies. Results demonstrate that combined bednet and treatment strategies achieve the greatest reduction in malaria incidence at acceptable cost-effectiveness thresholds defined relative to the Nigerian gross domestic product per capita. Sensitivity analysis of the basic reproduction number reveals mosquito biting rate as the most critical parameter for transmission control. Keywords: optimal control, malaria transmission, compartmental model, Pontryagin maximum principle, Kano State