In college, back in the 1970's, I had a professor of Effective Writing (i.e., Freshman Comp) who told us that "Language is Thought", and if you don't know how to express something clearly, it is because the thought isn't clear in your own mind. This discussion is really helping me clarify my own thinking on the matter.
The more I think about what my DTR really represents, the more I don't like how I've said it. I'm not sure I like the word "acceleration" as I've used it and as others are likely to understand it. I know I don't like the word "rate". It's not a "rate". It is a "rate of change".
So let's try this: the DTR in my model should be renamed "Adjusted Transmission Exponent (ATE)". It is an alternative way of expressing the rate of transmission, adjusted for the variations that have occured over time in the rate of transmission, both positive and negative. It "smooths out" the daily, weekly, and monthly variations in the rate of transmission to provide a single number that can be used as a mathematical exponent to project into the future, based on past transmission rates.
Glad I’m helping.
I’m still not sure that your exponent represents what you want it to represent. It seems to work. The projection 3 months out, is reasonable for a model that includes a positive increase to the rate of change. but without a clear understanding of what it represents, I’m not sure when you go out beyond 3 months that it’s still a valid model.
Try this. Try to express it as a simple day to day formula formula without exponents. Day1 = Day0*whatever+/-whatelse. If you can do that, we can test to see if the exponent formula is correct.
This isn't how real outbreaks progress. Things will change over time. Your DTR won't be constant. A real projection would have to model transmission rates as the disease moves into new territories and populations. But of course we won't really know how that's going to work until it happens.