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

T.A. Midhun and K. Murugesan

Chaos, Solitons & Fractals, 2025, vol. 191, issue C

Abstract: 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.

Keywords: Extinction; Ornstein–Uhlenbeck process; Probability density function; Sex-structured HIV/AIDS model; Stationary distribution (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:191:y:2025:i:c:s0960077924014516

DOI: 10.1016/j.chaos.2024.115899

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