The role of environmental contamination in the dynamics of HIV–TB co-infection with control strategies: Caputo fractional-order approach

This study investigates the effectiveness of integrated environmental and medical interventions in controlling HIV-TB co-infection. A Caputo fractional-order modeling framework is developed to capture memory and nonlocal effects inherent in chronic infections, while explicitly incorporating environmental reservoirs of Mycobacterium tuberculosis as an additional transmission pathway. The mathematical well-posedness of the model is established through existence, uniqueness, positivity, boundedness, and Ulam-Hyers stability analysis. Numerical solutions are obtained using an Adams-Bashforth-Moulton predictor-corrector scheme, and unknown parameters are calibrated using World Health Organization HIV-TB co-infection data from Tanzania spanning 2000-2023. The estimated fractional order is p=0.982, indicating strong memory effects that reflect the cumulative impact of past infection history, delayed immune responses, prolonged treatment effects, and persistent environmental contamination characteristic of HIV-TB co-infection dynamics. Model validation using an independent dataset from Kenya (2000-2023) demonstrates the robustness and geographic transferability of the proposed framework. Sensitivity analysis identifies key epidemiological parameters governing transmission and control, emphasizing the joint importance of clinical treatment and environmental sanitation. A comparative analysis between the fractional-order model (p=0.982) and the classical integer-order model (p=1) reveals that the fractional formulation provides an improved fit to observed data and captures long-term disease dynamics more accurately, particularly in reproducing persistent infection trends. Overall, the results show that coordinated medical interventions combined with environmental control substantially reduce HIV-TB co-infection prevalence, underscoring the necessity of integrated, multi sectoral strategies for sustainable disease management in high-burden settings.