Analysis of Fractional Order Mathematical Model of HIV-TB Using Atangana-Baleanu-Caputo Operator in the Presence of Treatment for TB

Analysis of Fractional Order Mathematical Model of HIV-TB

Résumé

This study investigates the transmission dynamics of HIV-Tuberculosis (TB) co-infection using a mathematical model that incorporates the Atangana-Baleanu-Caputo (ABC) fractional operator with the Mittag-Leffler kernel. The fractional framework allows for a more accurate representation of the complex and memory-dependent nature of disease progression and transmission. To ensure the validity of the model, the existence and uniqueness of its solutions were rigorously analyzed using the Picard-Lindelöf theorem. This theoretical approach guarantees the robustness and reliability of the mathematical model. To further understand the factors driving TB infection dynamics, we conducted comprehensive sensitivity and uncertainty analyses. These analyses focused on identifying the most influential parameters affecting disease transmission, with the basic reproduction number serving as the response function. Our findings highlight that the TB transmission rate, modification parameters accounting for the infectiousness of TB-only individuals, and treatment rates for individuals with latent TB infections were the primary drivers of TB spread within the population. Numerical simulations were performed to explore intervention strategies aimed at reducing the dual burden of HIV-TB co-infection. The results suggest that prioritizing treatment for individuals diagnosed with latent TB—whether infected with TB alone or co-infected with HIV—can significantly decrease both TB and HIV incidence in the studied population. This targeted approach demonstrates the critical importance of timely and focused treatment in mitigating the overall disease burden. Our study underscores the need for integrated healthcare interventions and highlights the utility of fractional-order models in capturing the nuanced dynamics of co-infections. These findings provide valuable insights for policymakers and healthcare providers seeking to design effective strategies to control the dual epidemics of HIV and TB.