Stationary distribution and near-optimal control of a stochastic reaction-diffusion HIV model

Considering stochastic perturbations and spatial diffusion in both virus-to-cell and cell-to-cell transmissions, a stochastic reaction-diffusion HIV model is developed. Firstly, the existence and uniqueness of a global positive solution and stationary distribution are demonstrated. Secondly, considering the effect of drug therapy on the disease, the control strategy is introduced into the stochastic HIV model. By employing Pontryagin's stochastic maximum principle, the sufficient and necessary conditions are obtained for near-optimal control. Finally, numerical simulations are reported to support and supplement our theoretical results.