MATHEMATICAL MODELING AND OPTIMAL CONTROL ANALYSIS OF HUMAN AFRICAN TRYPANOSOMIASIS TRANSMISSION WITH RELAPSE RESPONSE

Human African Trypanosomiasis (HAT), a neglected tropical disease transmitted by tsetse flies, remains a health issue in sub-Saharan Africa. This study develops a seven-compartment mathematical model that includes human and vector dynamics, along with relapse mechanisms. The model's consistency is confirmed through boundedness and positivity analysis. Equilibrium points are calculated, and stability is discussed. The transmission potential via the basic reproduction number, R₀ was derived. An optimal control framework integrates three strategies: public awareness, regular screening and treatment, and vector control with insecticide traps. Using Pontryagin’s Principle, cost-effective approaches are identified to reduce infections. Simulations show that combined interventions effectively lower HAT prevalence, with relapse management preventing resurgence. The findings highlight the importance of coordinated, timely strategies and relapse-aware healthcare, providing valuable insights for policymakers to implement resource-efficient measures for HAT elimination.