Advancing Epidemiological Modeling: Spectral Collocation for Sleeping Sickness

While nonlinear ordinary differential equations (ODEs) are fundamental to epidemiological modeling, they require numerical solvers that are both accurate and stable over long-term simulations. This study addresses this gap by implementing and validating a Chebyshev-based Spectral Collocation Method (SCM) for a nonlinear model of Human African Trypanosomiasis (HAT, or sleeping sickness). The numerical scheme's stability is ensured by a row replacement strategy used to correctly impose the system's initial conditions. The method's accuracy is demonstrated by computing the residual errors and through direct validation against an ODE solver. Using this validated model, qualitative and quantitative global sensitivity analyses were performed. The analysis identified the tsetse fly mortality rate ($\omega$) as the most influential parameter governing disease outcomes. This finding strongly suggests that targeted vector control is a highly effective intervention strategy. This work demonstrates that the SCM can be a useful tool for epidemiological modelers and the public health community.