The impact of treatment accessibility on HIV-TB co-infection: a comparative fractional-order modeling approach.

HIV-tuberculosis (TB) co-infection remains a major global health challenge, especially in regions with limited treatment accessibility. This study presents a fractional-order mathematical model that captured the transmission dynamics of HIV-TB co-infection among treated and untreated populations, incorporating disease progression through multiple compartments. The model is examined using three distinct fractional derivative operators, the Caputo derivative (power-law kernel), the Caputo–Fabrizio derivative (non-singular kernel), and the Atangana–Baleanu derivative (Mittag-Leffler kernel) to assess how memory effects influence infection dynamics. Treatment accessibility is represented as a factor modifying treatment and recovery rates, reflecting the proportion of infected individuals able to obtain timely medical care. Numerical simulations showed that dually infected populations experience significantly higher infection peaks compared to singly infected populations. This reflects a model-based result showing that, under the simulated parameter settings, the co-infection dynamics naturally produce higher peaks in dually infected groups than in singly infected populations. Variations in fractional orders (0.95, 0.85, and 0.75) significantly affect the temporal behavior and persistence of infection. Parameter values derived from current epidemiological data provide insight into the critical role of treatment accessibility in disease control. Numerical plots of the basic reproduction number () against key parameters illustrate that contact rates, treatment intensity, and accessibility levels strongly influence disease spread.The comparative operator analysis shows that expanding treatment accessibility consistently suppresses infection peaks across all fractional formulations, identifying it as the most effective and robust policy lever for controlling HIV–TB co-infection in resource-limited settings.Clinical trial numberNot applicable.