Stability analysis and optimal control for an age-structured HIV/AIDS reaction-diffusion model with inflammatory cytokines

In this paper, we establish and analyze an age-structured HIV reaction-diffusion model with inflammatory cytokines. We have derived the expression form of the basic reproduction number and proved that the solution of the model is bounded and unique. It has been shown that when 𝕽 0 is less than 1, there exists a globally stable disease-free equilibrium point, and when 𝕽 0 is greater than 1, the disease will persist uniformly. In addition, we have developed the optimal control problem and obtained the optimal control strategy based on the treatment of HIV virus. Finally, we conducted numerical simulations, and the simulation results were consistent with the theoretical results.