African trypanosomiasis is a disease that is spread through the bites of an infected tsetse fly. This study proposes a nonlinear mathematical model of African trypanosomiasis that includes humans, cattle, and tsetse flies in the presence of immigrants. The model also incorporates treatment, tsetse trapping, and public health education as potential control measures to give insight into the transmission dynamics of the disease. The effective reproduction number ( \(R_e\) ), a threshold used to determine whether the disease remains or dies out in the population, was calculated using the Next Generation method. It is observed that the disease-free equilibrium point is locally and globally asymptotically stable when \(R_e~<~1\) and unstable otherwise. Moreover, using the normalized forward sensitivity index method, the sensitivity analysis of the model parameters was carried out to determine the most influential parameter. The results show that the tsetse fly biting rate is the most sensitive parameter to the effective reproduction number. Furthermore, the numerical simulations of the model show that public health education, treatment, and tsetse-fly traps have the positive effects of reducing disease transmission in the community. However, it is also observed that the presence of infected immigrants increases the disease prevalence in the population. The numerical simulation also revealed that the presence of infected immigrants in the population increases the endemicity of the disease. The study suggest that if we are to eliminate African trypanosomiasis in the population, there should be a program of screening the immigrants to identify the infected individuals to avoid the disease transmission.
