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Result 1998-1999 epidemic 2 SIR model Baseline Different Alpha BFGS (neg fast C code)
For the guess of parameters beta1 = 1.1 alpha1 = 1 Ne = 7763.228 I1 = 1 beta2 = 1.1 alpha2 = 1 I2 = 1, we obtained
beta1 = 3.372741e+02 alpha1 = 3.366537e+02 Ne = 3.414239e+04 I1 = 1.693020e-02 beta2 = 8.714923e+00 alpha2 = 8.408702e+00 I2 = 2.000415e-01
So, this implies that f = 3.414239e+04/30433887 = 0.001121854
The MLE was -143.39
The confidence intervals for the coefficients
2.5 % 97.5 %
beta1 3.328939e+02 3.383710e+02
alpha1 3.355832e+02 3.408790e+02
N 2.299527e+04 6.341676e+04
I1 2.933891e-02 8.711653e-02
beta2 8.612250e+00 8.855954e+00
alpha2 8.264357e+00 8.634177e+00
I2 9.287987e-02 4.111497e-01
r 1.002736e+03 1.775357e+03
So, r = 298.2902.
AICc value 308.5382
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).
epi102dabfgsac1n_regional_.pdf
Here are the two SIR models, overall data, and laboratory data (blue is the type A flu data, green is the type B flu data).
Weston: This is the first model fit where the two SIR models do not really correspond to the laboratory data.