A mathematical model based on ABC fractional order for TB transmission with treatment interruptions in case of Bule Hora town, Ethiopia

Abstract

In this study, we introduce a novel fractional-order model enriched with the Atangana-Baleanu-Caputo derivative to explore the dynamics of TB transmission in developing nations, where tuberculosis (TB) remains a pressing public health concern requiring urgent attention. We outline the methodology employed, emphasizing key aspects such as solution existence, uniqueness, Hyers-Ulam stability, and numerical simulations. Equilibrium points of the system, including the Disease-Free Equilibrium (DFE) and the Endemic Equilibrium (EE), are revealed through adopted mathematical manupulations. Following rigorous numerical simulations employing the Euler approach and a meticulously crafted scheme, the study illustrates compartmental solutions across a spectrum of fractional orders. This approach provides a comprehensive understanding of the model’s behavior and its responsiveness to different parameter configurations. Remarkably, as the fractional order tends towards one, our findings align closely with those of traditional integer-order models, offering insightful parallels into the model’s dynamics. Additionally, our work emphasizes the pivotal role of vaccination as a preventive measure, elucidating its profound impact on reducing tuberculosis incidence within communities. The promotion of widespread access to TB vaccines emerges as a potent strategy in curtailing the disease’s prevalence, underscoring the significance of proactive vaccination initiatives. As conclusion, this study presents a comprehensive examination of TB dynamics through a fractional-order modeling approach. Our results pave the way for further exploration, including the investigation of alternative fractional-order derivatives and exploration of theoretical and numerical stability. These endeavors will enhance our understanding of TB dynamics and inform more effective strategies for disease control and prevention.