Modeling HIV/AIDS with the effect of screening in India: A stochastic sex-structured approach incorporating logarithmic mean-reverting Ornstein–Uhlenbeck process

This study introduces a novel stochastic sex-structured HIV/AIDS model with the effects of screening the infectives incorporating the Ornstein–Uhlenbeck process, specifically suitable to the Indian demographic context. Firstly, we prove the existence of a unique positive global solution, thereby ensuring the stochastic model is well-defined. Further, we establish sufficient conditions for infection extinction through the stochastic extinction parameter R0e, indicating that the infection will die out if R0e<1. Conversely, the persistence of the infection is demonstrated by the existence of a stationary distribution of the solution when the stochastic threshold R0s>1, achieved through the appropriate selection of Lyapunov functions. In addition, we investigate the expression of the approximate probability density function of the stationary distribution around the quasi-endemic equilibrium point. Also, real-world data on people living with HIV in India from 2010 to 2022 is fitted to the stochastic model, which in turn provides region-specific parameter values. Our theoretical findings are subsequently validated through numerical simulations. Finally, we suggest effective control strategies for India based on model predictions and sensitivity of key parameters.