Optimal Control Theory Applied to Tuberculosis Treatment Adherence Programmes in Katsina State

Tuberculosis treatment non-adherence in Katsina State, North West Nigeria, is a major driver of treatment failure, drug resistance development, and continued community transmission, with the state reporting a treatment success rate of 76 percent against the national target of 90 percent. This study applies optimal control theory to a Susceptible-Exposed-Infected-Treated compartmental model to identify the time-optimal strategy for allocating directly observed therapy resources and community health worker interventions across the state's 34 Local Government Areas. The optimisation objective minimises total infection burden and treatment cost over a five-year planning horizon. Pontryagin's Maximum Principle is applied to derive necessary conditions for the optimal control, which is characterised as a combination of intensive community outreach and differentiated DOTS supervision intensity. Numerical solution is implemented using the forward-backward sweep method in MATLAB. Results demonstrate that front-loading community health worker deployment in the first 18 months reduces cumulative incidence by 43 percent compared to uniform resource distribution over the planning horizon. The optimal strategy requires 22 percent higher initial expenditure but achieves 35 percent lower total five-year cost through faster case detection and reduced retreatment requirements. Keywords: optimal control, tuberculosis, treatment adherence, Katsina State, Pontryagin's principle.