Analysis of a TB and HIV co-infection model under Mittag-Leffler fractal-fractional derivative

Xuan Liu, Shabir Ahmad, Mati ur Rahman, Yasir Nadeem, Ali Akgül

2022Physica Scripta21 citationsDOI

Abstract

Abstract 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 Krasnoselskii 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.

Topics & Concepts

FractalFractional calculusMathematicsHuman immunodeficiency virus (HIV)Fixed-point theoremKernel (algebra)Operator (biology)Applied mathematicsFixed pointInvariant (physics)Stability (learning theory)Pure mathematicsMathematical analysisMathematical physicsVirologyComputer scienceMedicineBiologyGeneBiochemistryTranscription factorMachine learningRepressorFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisMathematical and Theoretical Epidemiology and Ecology Models