We had been trying to do this ourselves but found this fun model: https://gabgoh.github.io/COVID/index.html
We can attest that the model parameters agree with our own incomplete efforts. It has lots of fun stuff to play with, and you can test the sensitivities of all the variables. We disagree with the commonly assumed R(initial) value ~2.5. The table of calculated values on the site has an average of 4.5. An excellent paper in review, Sanche et al at Los Alamos available on the CDC website finds Ri over 5. This model goes completely off the rails at these values so we set close to 3. We also disagree with a short infectious duration. Symptomatic spread alone is at least 5 days and there are at least 3 days of asymptomatic. Surprisingly, the model is insensitive to infectious duration, merely shifting the timing. Above we set the model to as close as possible to N=1 million so for the US you multiply by 327. The model seems excessively sensitive to initial infections. By limiting to 1 million and 1 initial behavior improved. Hospitalizations are a reasonable match, but deaths are too low. What we like about this is that contrary to the IHME model which predicts a decline that has not materialized, this shows we are going to be dealing with this for a while.
Above we tried to coax the model to replicate data we have for deaths and hospitalizations. We know from the Covid Tracking Project and Worldometers that daily hospitalization accelerated to 79,000 about April 15 and have declined only slightly since ever since, defying the IHME model’s projected decline. Daily deaths reached a high of 2800 about April 20, and have likewise failed to decline according to IHME.
We were able to get a reasonably sensible approximation of actual US hospitalization and death only by removing intervention altogether. This makes no sense as intervention must surely be a factor. The model also takes way too long to reach appropriate values. We are seemingly only two months in.
We have developed some sympathy for the difficulty of modeling, but are forced to conclude that important variables are not yet included.