University of Guilan Journal of Mathematical Modeling 2345-394X 2026 05 18 Fractional order optimal control of a tuberculosis model with exogenous reinfection 9612 10.22124/jmm.2026.32379.2933 EN Maryyam Irfan Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan Mustafa Habib Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan Shazia Karim Department of Basic Sciences, UET Lahore, FSD Campus, Faisalabad, Pakistan Muhammad Shabbir Department of Mathematics, University of Engineering and Technology Lahore Journal Article 2025 11 25 This paper presents a general formulation of a fractional-order tuberculosis model with exogenous reinfection, based on the susceptible–exposed–infected–treated (SEIT) epidemiological framework. A control representing the prevention of exogenous reinfection is employed to effectively minimize the number of infectious individuals, including both actively contagious and latently infected populations. The Caputo fractional derivative is used to model the system, and the resulting fractional-order optimal control problem is theoretically analyzed using Pontryagin’s maximum principle. A forward-backward sweep algorithm, using a generalized Euler method, is applied to numerically solve the optimality system. Numerical simulations demonstrate the efficiency and effectiveness of the proposed optimization procedure. https://jmm.guilan.ac.ir/article_9612_474a2dbb302f2d9dfbf694b5215d162a.pdf