Controlling the Transmission Dynamics of HAT Incorporating Impacts of Temperature

Human African Trypanosomiasis (HAT) remains a persistent public health threat in sub-Saharan Africa, with transmission dynamics tightly coupled to the ecology and physiology of its tsetse fly vector. Despite growing evidence that temperature strongly modulates vector survival, development, and biting behavior, most existing transmission models assume static environmental conditions. We develop a model for HAT that incorporates temperature-dependent vector recruitment, mortality, and biting rates, thereby mechanistically linking environmental variability to epidemiological outcomes. The model couples human and tsetse populations and admits both disease-free and endemic equilibria. Using the next-generation matrix approach, we derive an explicit expression for the basic reproduction number and show that it depends nonlinearly on temperature through multiple entomological pathways. Bifurcation analysis reveals a forward transcritical bifurcation, indicating a clear threshold for disease persistence. Our findings demonstrate how temperature can fundamentally alter transmission potential and control thresholds, highlighting the importance of integrating climate-sensitive vector biology into HAT risk assessment and intervention planning under ongoing environmental change.