Fractional epidemic model analysis and control of multidrug-resistant and extensively drug-resistant tuberculosis

Tuberculosis (TB) continues to be a major public health concern in China, worsened by the increase in multidrug-resistant strains (MDR) and extensively drug-resistant strains (XDR). To address this, we propose a mathematical approach that includes memory effects to model the dynamics of TB transmission and drug resistance. Using the Caputo fractional derivative and Diethelms method, we construct a fractional order model and analyze the stability of disease-free and endemic equilibrium points. The basic reproduction number is derived using the next-generation matrix method. To solve the fractional model, we employ the Adams–Bashforth–Moulton predictor–corrector method and estimate the best parameters using tuberculosis data from 2000 to 2022 in China, applying the Levenberg–Marquardt algorithm with MATLAB’s fitnlm function. The threshold parameter [Formula: see text] was found to be less than one for China, demonstrating that the fractional model provides superior prediction, analysis and parameter estimation compared to classical models. These findings indicate that incorporating memory effects into TB models can deepen our understanding of disease dynamics and improve the effectiveness of intervention strategies, ultimately helping to manage and control MDR and XDR TB in China.