A Comprehensive Analysis of Fractional-Order Model of Tuberculosis with Treatment Intervention

Tuberculosis (TB) remains one of the top infectious disease killers worldwide, with an estimated 10.6 million new cases and 1.3 million deaths reported in 2022 alone (WHO, 2023). The COVID-19 pandemic has further disrupted TB control efforts by limiting access to healthcare services, interrupting treatment regimens, and delaying diagnoses leading to a resurgence in TB transmission It is caused by Mycobacterium tuberculosis and spread through the air, TB poses a serious threat, particularly to vulnerable groups such as individuals with weakened immune systems, including those living with HIV. These challenges emphasize the need for more robust and realistic modeling approaches to inform policy and intervention. In this study, we developed a fractional-order mathematical model to better understand how TB spreads and how it can be controlled. Our model divides the population into six key groups: those susceptible to infection, exposed individuals, people with acute TB, those with chronic TB, individuals undergoing treatment, and those who have recovered. To capture the complexities of TB transmission, we incorporated fractional-order derivatives along with the Adams-Bashforth method, allowing us to account for memory effects and more accurately reflect real-world dynamics. Through sensitivity analysis, we found that increasing treatment rates significantly boosts recovery among infected individuals. Our simulations also explored various intervention strategies, such as improving access to treatment, reducing diagnostic delays, and addressing non-linear transmission patterns. The results highlight the effectiveness of these measures in curbing TB spread and offer insights for improving disease control efforts.