Mathematical models and statistical models

I suppose I started thinking about this really hard in the early days of the COVID-19 pandemic. I’m not sure it’s something we articulate well; the difference between a mathematical model. A mathematical model is meant to capture the science of a phenomenon in mathematical terms. A statistical model is meant to “fit” data and account for the uncertainty; but doesn’t necessarily explain the science. And there are certainly plenty of examples where you’re fitting a …