For the US as of 20200719, the best fit SEIR model is shown as:


Optimized SEIR model for the current corona virus evolution for the US
Associated operational parameters:
\(S_0\) = 3.239941e+07 cases;
\(\beta\) = 2.110975e06 (cases days)\(^{1}\);
\(\sigma\) = 9.268004e04 days\(^{1}\);
\(\gamma\) = 1.498313e02 days\(^{1}\).
These translate into the more familiar parameters:
R = 4564.757255;
T\(_{inc}\) = 1078.980945 days;
T\(_{inf}\) = 66.741736 days.
The additional initial values were:
\(E_0\) = 1.50e+01, \(I_0\) = 1.20e+01, \(R_0\) = 3.00e+00.
As a measure of quality of the convergence of the annealing algorithm, the final error measure was:
\(\epsilon\) = 1.119641e+05 cases; with a relative error, \(\epsilon/S_0\) = 3.46e03 or 0.3%
