# What's the correct regression model for a contagious disease like COVID-19?

I'm examining how COVID-19 has struck different states asymmetrically, with some in the early stages of growth and others in which the number of daily cases is now coming down. Here's what the national day-by-day data looks like, with a seven-day moving average as the red line:

I think the best way to classify 51 different curves is to use a regression model that can be applied to each state, and then see how the coefficients compare to the national model. But I'm at a loss as to the appropriate type of regression to use. As best I can tell, it's exponential up to the peak and then becomes logarithmic. Which is to say, if a * b^x is the model, b is not constant and eventually becomes fractional.

I've looked a bit into the literature of epidemiology models, but haven't found anything straight-forward enough to suit these purposes.

• Since this is count data, a poisson regression might be a good fit. Apr 30, 2020 at 21:15
• You can fit a simple line or curve, but I doubt it would tell you much. Mechanistic models are still likely to be the best approach. But if you want to visually compare states, there's plenty of visualisation methods out there e.g. time since ~n cases (n = 10 or 100 usually) on the X-axis and log(cases) on the Y-axis.
– mkt
Apr 30, 2020 at 21:40