Sensitivity analysis of Human Africa Trypanosomiasis with human host

Сажетак

Human African Trypanosomiasis (sleeping sickness) remains a significant public health challenge in sub-Saharan Africa, transmitted through the bite of infected tsetse flies. To better understand its transmission dynamics, we develop a compartmental SEIR model that accounts for both human and tsetse fly populations, incorporating varying transmission rates between exposed and infectious individuals — a key feature often overlooked in prior studies. Using the next-generation matrix method, we derive the basic reproduction number (R0), a critical threshold for disease persistence. We establish the positivity, boundedness, and existence and uniqueness of solutions, ensuring the mathematical well-posedness of the model. A normalized forward sensitivity analysis identifies the most influential epidemiological parameters, providing insights for targeted intervention strategies. In particular, parameters related to tsetse fly - human transmission rates (β1, β2) and human treatment rate (βh) showed the highest sensitivity indices, indicating their strong influence on R0 and overall disease spread. We also analyze the disease-free and endemic equilibria, demonstrating that R0 governs the long-term behavior of the system. Numerical simulations validate our
analytical findings and illustrate how variations in transmission rates, vector control, and treatment efficacy shape disease dynamics. Our results underscore the importance of adaptive intervention strategies in mitigating Trypanosomiasis outbreaks and inform public health policies for sustainable disease control.