A stochastic reaction-diffusion HIV/AIDS model with implications for long-Acting ART.

This study proposes a stochastic reaction-diffusion model for HIV/AIDS transmission to uncover the foundational mechanisms behind disease extinction and project the future trajectory of the pandemic. For the proposed model, we initially apply the idea of the Zvonkin transformation to establish a novel analytical framework. Subsequently, the existence and uniqueness of a globally positive solution were demonstrated by reformulating the problem within the context of a reaction-diffusion equation. Furthermore, we establish sufficient conditions for disease persistence by constructing an appropriate Lyapunov function. Within a specific parameter regime, we also prove that the disease becomes extinct at an exponential rate. More importantly, by leveraging the latest advances in long-acting antiretroviral therapy (LA-ART) and stochastic modeling theory, we derive the stationary distributions and probability density function for the theoretical zero mortality rate from AIDS-induced death. And, a series of numerical simulations is conducted to validate the theoretical findings. The simulation results confirm that a specific level of noise is sufficient to cause the disease to die out exponentially. Theoretical analysis predicts that AIDS will continue to pose a major public health threat, with its asymptomatic stage being a critical determinant of the disease's overall trajectory. Consequently, future efforts must prioritize this stage. A deeper investigation into its underlying mechanisms is essential to develop targeted interventions.