In this paper, the nonlocal operator with the Mittag-Leffler kernel is used to analyze a TB-HIV co-infection model with recurrent TB and exogenous reinfection. The non-negative invariant region and basic reproduction number of the proposed model are demonstrated. By using the Krasnosel- skii fixed result, we investigate that the TB-HIV co-infection model possesses at least one solution. We look at the existence of a unique solution using Banach’s fixed point theorem. Functional analysis is used to demonstrate Ulam-Hyres stability. The numerical solution of the given model is obtained using the Adams-Bashforth technique. We illustrate the achieved results by studying the co-infection of TB and HIV for different fractional and fractal orders.

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