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

• Published in: Informatics in medicine unlocked 2024, Vol.47, p.101498, Article 101498
• Main Authors: Sado, Abdulsamad Engida, Kotola, Belela Samuel
• Format: Article
• Language: English
• Subjects: Disease transmission dynamics; Fractional-order modeling; Tuberculosis; Vaccination and Public health
• ISSN: 2352-9148; 2352-9148
• DOI: 10.1016/j.imu.2024.101498

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 manipulations. 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. •Study highlights on tuberculosis spread using fractional-order model.•Developed a novel TB model with ABC fractional derivative, including two treatment classes and a linear incidence function.•Validated model’s mathematical robustness with existence and uniqueness of solutions and employed Hyers-Ulam stability analysis.•Conducted numerical simulations using Euler approach, exploring vaccination and treatment impacts on infection rates.