Mathematical model for trypanosomiasis management integrating treatment enhancement, vector control, and host management strategies

Human African Trypanosomiasis (HAT) remains a persistent public health challenge due to its complex zoonotic transmission cycle and high endemic potential. This study introduces a mathematical model that explicitly integrates stage-specific human clinical progression with a dynamic cattle reservoir and mechanistic vector control to evaluate intervention strategies within a One Health framework. Comprehensive analysis using the normalized forward sensitivity index and Latin Hypercube Sampling-Partial Rank Correlation Coefficient (LHS-PRCC) identifies the cattle cycle as the dominant transmission pathway, contributing approximately 97.8% of the overall epidemic risk. Notably, cattle treatment was identified as the most influential single lever for reducing the basic reproduction number, while the tsetse biting rate and mortality remain the primary environmental drivers of infection. Numerical simulations validate these theoretical findings, demonstrating that single interventions are insufficient for sustained elimination. While human treatment provides essential clinical benefits by rapidly reducing morbidity, its impact on the population-level epidemic threshold is negligible. Conversely, integrated cattle treatment and vector control are highly effective at clearing the primary animal reservoir and infectious vector pools. The model decisively demonstrates that only a combined strategy, leveraging animal reservoir clearance alongside immediate clinical care, can successfully drive disease prevalence to a near-zero state. Consequently, this study recommends a policy shift from human-centric care to an integrated host-vector management framework. Prioritizing interventions at the cattle-vector interface is essential to meet the World Health Organization (WHO) 2030 targets and achieve sustainable local elimination.