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Result 1989-1990 epidemic 2 SIR model Baseline Different Alpha BFGS Jul (neg fast C code)
For the guess of parameters beta1 = 0.3 alpha1 = 0.2 Ne = 3876.95 I1 = 1 beta2 = 0.3 alpha2 = 0.2 I2 = 1, we obtained
beta1 = 1.327932e+01 alpha1 = 1.246641e+01 Ne = 7.057050e+03 I1 = 2.074622e-01 beta2 = 2.619515e+01 alpha2 = 2.556590e+01 I2 = 1.609588e-03
So, this implies that f = 7.057050e+03/27653146 = 0.0002551988
The MLE was -72.4
The confidence intervals for the coefficients
2.5 % 97.5 %
beta1 1.324312e+01 1.385137e+01
alpha1 1.203896e+01 1.250278e+01
N 6.169583e+03 7.650427e+03
I1 1.408222e-01 5.115786e-01
beta2 2.587132e+01 2.629264e+01
alpha2 2.546973e+01 2.610079e+01
I2 2.351165e-03 8.002798e-03
r 4.390481e+09 5.026102e+09
So, r = 9,335,707.
AICc value 175.1937
Weston: All of these values almost exactly match the ones given by having the Poisson distribution happen after r > 1,000,000.
Here’s a plot of the model with the data (black is the data, blue is the sum of the two models and baseline, red is the first SIR model, yellow is the second SIR model, and orange is the baseline)
Here are the two SIR models, overall data, and regional data (blue is the BC data, green is the Ontario data, and purple is the Quebec data).