Differential epidemic models and scenarios for restrictive measures

We consider algorithms for calculating the spread of epidemics and analyzing the consequences of introducing or removing restrictive measures based on the SIR model and the Hamilton–Jacobi–Bellman equation. After studying the identifiability and sensitivity of the SIR models, the correctness in the neighborhood of the exact solution and the convergence of the numerical algorithms for solving forward and inverse problems, the optimal control problem is formulated. Numerical simulation results show that feedback control can help determine vaccination policies. The use of PINN neural networks reduced the computation time by a factor of 5, which seems important for promptly changing restrictive measures.