Abstract:

A tuberculosis transmission model with diffusion factors was established, introducing four control variables: increasing personal protective awareness, timely detection and treatment, improving treatment level, and reducing recurrence rate. The optimal control problem was discussed theoretically and numerically. Firstly, the existence of optimal control was obtained using the optimal control theory of partial differential equations. Secondly, the characteristics of optimal control were calculated by constructing sensitivity systems and adjoint systems. Finally, the variation of optimal control variables over time was demonstrated through numerical simulations, and the optimal control effect was shown. The results showed that compared with the uncontrolled situation, optimal control can significantly reduce the number of latent, infected, and treated individuals at the termination of control; Compared to a single control scenario, optimal control can reduce the peak of infected individuals, delay peak time, and decrease the final number of infected individuals. The conclusion drawn can provide a theoretical reference for frontline disease prevention and control.

Key words: tuberculosis, diffusion model, optimal control, numerical simulation