The coronavirus disease, COVID-19, has become a global challenging pandemic. Causing significant loss of life, property, and economics worldwide. The study of infectious disease models allows us to have a deeper understand of spreading trend of highly infectious diseases. Therefore, studying infectious disease models is imminent. In this work, we propose learning spacial domain infectious disease control model for vaccine distribution by physics-constraint machine learning. Usually, these dynamical systems are utilized in epidemiology models to predict the time evolution and development trend of highly infectious diseases such as COVID-19. We reformulate the SIR models and give corresponding policies via dynamical systems. More importantly, we obtain the approximating numerical solution of the systems of dynamical PDEs via the PINNs algorithm, within the acceptable range of approximation error. Additionally, we present several numerical solutions of the PDEs under a variety of scenarios.