Analysis of fractional order mathematical model of HIV-TB using Atangana-Baleanu-Caputo operator in the presence of treatment for TB

Agbata Benedict Celestine; Raimonda Dervishi; Erjola  Cenaj; Habeeb A. Aal-Rkhais; Marcos  Salvatierra; Shyamsunder; Bolarinwa  Bolaji

doi:10.5269/bspm.75875

Agbata Benedict Celestine
Raimonda Dervishi
Erjola Cenaj
Habeeb A. Aal-Rkhais
Marcos Salvatierra
Shyamsunder SRM University Delhi-NCR, Sonepat
Bolarinwa Bolaji

Abstract

This study presents a mathematical investigation of the transmission dynamics of HIV - Tuberculosis (TB) co-infection using the Atangana-Baleanu-Caputo (ABC) fractional operator with MittagLeffler kernel, representing a significant advancement over conventional integer-order models by capturing the memory-dependent nature of disease progression that traditional approaches cannot adequately represent. The model’s mathematical rigor was established through existence and uniqueness analysis using the PicardLindelöf theorem, ensuring solution reliability. Comprehensive sensitivity and uncertainty analyses, with the basic reproduction number as the response function, identified three critical parameters driving TB transmission: the TB transmission rate, modification parameters for TB-only individual infectiousness, and latent TB treatment rates. Numerical simulations demonstrated that prioritizing treatment for individuals with latent TB infections—both TB-only and HIV-TB co-infected cases—significantly reduces both TB and HIV incidence rates in the population. The fractional-order framework successfully captures nuanced co-infection dynamics that conventional models miss, while our intervention analysis reveals that targeted treatment of latent TB infections represents a highly effective strategy for controlling the dual HIV-TB epidemic, providing evidence-based guidance for integrated healthcare policies.

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