Look into random graph models. Or exponential random graph models. Mathematical models are difficult because we don’t know the real inputs and fitting a curve

Look into random graph models. Or exponential random graph models. Mathematical models are difficult because we don’t know the real inputs and fitting a curve in retrospect is easy to get a compelling looking answer which is wrong. You can gain an intuition for it just imagining a random walk on a social network graph though. Just jump from friend to friend randomly on Facebook. Early on it is easy to spread to new people. Later on it’s very difficult to find new people. You get stuck in the same cohorts. More simply just look at past covid outcomes. Or pretty much any epedemiological model. All of them claim only the initial period is exponential. It’s the issue of how to determine the slowdown period that’s tricky and frankly impossible without more data than we have. But assuming that the slowdown state will look similar to previous slowdown states is a good idea.