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Result 1989-1990 epidemic 2 SIR model Baseline Different Alpha BFGS Jul (poi/neg 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 = 2.395862e+01 alpha1 = 2.332746e+01 Ne = 6.426984e+03 I1 = 1.710170e-03 beta2 = 1.202747e+01 alpha2 = 1.121492e+01 I2 = 2.301870e-01
Weston: This is odd indeed because I figured this one should return nearly the same parameter values as the model from Jul 9th. It seems to me that the negative binomial results were right (seeing as almost all the parameters here except alpha2 are close to the negative binomial ones, whereas not near to the Jul 9th results). Also, it appears that although the program finished, the results did not converge because of the missing values in the returned confidence matrix.
So, this implies that f = 6.426984e+03/27653146 = 0.0002324142
The MLE was -72.4
The confidence intervals for the coefficients
2.5 % 97.5 %
beta1 2.324402e+01 NA
alpha1 NA 2.370409e+01
N 5.586697e+03 6.963144e+03
I1 3.026114e-03 1.372460e-02
beta2 1.199164e+01 NA
alpha2 NA 1.125105e+01
I2 1.520733e-01 5.706966e-01
It switched to a Poisson distribution when r > 10,000.
AICc value 168.9891
Weston: This AICc value is lower than the result for Jul 9th, 169.1047, which implies it had a better fit. This supports the idea that the negative binomial distribution discovered a better fit.
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).