MODELING AND STABILITY ANALYSIS OF FRACTIONAL HUMAN AFRICAN TRYPANOSOMIASIS DYNAMICS WITH OPTIMAL CONTROL

Human African trypanosomiasis (HAT), a vector-borne disease caused by the Trypanosoma brucei parasite, continues to pose significant public health challenges in Sub-Saharan Africa. This paper introduces a novel fractional-order mathematical model that incorporates optimal control options, such as vaccine, treatment, and sanitation measures, while capturing the intricate dynamics of HAT transmission. The model takes into consideration historical interactions and memory effects that may be missed by more typical integer-order models using fractional calculus. The boundedness of the model is established, showing that all of its solutions with beginning conditions stay inside the region. This suggests that the model is positively invariant and epidemiologically properly posed. To ensure our model’s empirical relevance and dependability, we validate it using actual incidence data from the World Health Organization. We determine crucial equilibrium points and evaluate the effects of different control techniques on disease prevalence using a thorough stability analysis. The results of the sensitivity analysis demonstrate that the ( \(\mathcal {R}_{0}\) ${\mathcal{R}}_0$ ) is highly impacted by effective contact rates, with larger rates signifying the necessity of managed disease control. Our results show that disease control efforts are much improved by a multifaceted approach that integrates vaccinations, treatment, and sanitation. In furtherance of adding to the theoretical understanding of HAT dynamics, this research offers useful information to public health experts and policymakers who want to maximize resource allocation and put into practice efficient disease management plans.