Global Stability and Optimal Control Analysis of Human African Trypanosomiasis Transmission dynamics with Two stages Infection

Abstract

A Mathematical model describing the transmission dynamics and optimal control of Human African Trypanosomiasis (HAT) is developed and analyzed. It is a neglected tropical disease transmitted by tsetse flies, continues to be a public health problem in sub-Saharan Africa. This study proposes an eight-compartmental mathematical model incorporating human and vector dynamics, with a relapse. The boundedness and positivity of the solution were discussed to show that the model is both mathematically consistent and biologically meaningful. The equilibria points (disease-free and endemic equilibrium) were calculated. The global stability analysis identifies disease-free and endemic equilibria, with the basic reproduction number R₀ of both derived to assess transmission were discussed. An optimal control framework is applied to optimize intervention strategies, three time-dependent controls were integrated: public awareness, regular screening and prompt treatment to mitigate further spread, and vector control using insecticide-treated traps. Pontryagin’s Maximum Principle was used for the analysis. The results demonstrate that strategically timed, integrated approaches such as public awareness, regular screening and prompt treatment, prioritizing vector reduction, and relapse aware healthcare prove most effective. This study provides good insights for policymakers, advocating for adaptive, resource efficient strategies to accelerate HAT elimination.