Fractional order optimal control of a tuberculosis model with exogenous reinfection

Irfan, Maryyam; Habib, Mustafa; Karim, Shazia; Shabbir, Muhammad

doi:10.22124/jmm.2026.32379.2933

Fractional order optimal control of a tuberculosis model with exogenous reinfection

Articles in Press

Document Type : Research Article

Authors

¹ Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan

² Department of Basic Sciences, UET Lahore, FSD Campus, Faisalabad, Pakistan

³ Department of Mathematics, University of Engineering and Technology Lahore

10.22124/jmm.2026.32379.2933

Abstract

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.

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