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. 
 A: There's no such a thing as "correct regression model" in here. You can fit many different curves to such data (like this, Gaussians, polynomials, exponential, or logistic curves etc.), neither of which will be based on realistic assumptions about underlying process. What follows, they will fit better, or worse, but they won't give you realistic grounds for making any but the short term predictions, or for explaining what, or why is going on. Moreover, the dynamics of growth of such epidemic depend on many moving parts: not only the dynamics of spread of the disease, but also people's actions, social distancing policies, healthcare response etc., that all change in time and are not heterogeneous. Still simplified, but more realistic models in epidemiology are based on mechanistic models (see e.g. this paper by Grassly and Fraser, 2008), not regression.
Of course, this doesn't mean that you cannot use regression models to study parts of such problems at all. You can always study local problems like "the growth rate was approximately constant in some period of time, and then it changed, what can be explained by some event" using regression models. Here same rules would apply like to modeling any other data using regression models. However in such cases we wouldn't use those models because of them being "correct", but because they might be useful.
