It’s not about an abstract model, there are feedback loops involved. Shutdowns and people’s behavior responds to the number of new infections. Globally across the last 6 months, new infections are close to 1:1 because you don’t exponential growth. Just look at the three waves in the US.

In effect masks buy you a more open environment where people can leave their homes and do more stuff. Further, when locations decide to shutdown that shutdown is more effective.