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Result 1996-1997 epidemic 2 SIR model Baseline Same Alpha BFGS (neg fast C code)
For the guess of parameters beta1 = 0.3 alpha1 = 0.2 Ne = 7918.306 I1 = 1 beta2 = 0.3 I2 = 1, we obtained
beta1 = 7.361329e+00 alpha1 = 6.992337e+00 Ne = 7.918396e+03 I1 = 1.593880e-03 beta2 = 7.654764e+00 I2 = 1.183821e-03
So, this implies that f = 7.918396e+03/29888998 = 0.0002649268
The MLE was -167.54
The confidence intervals for the coefficients
2.5 % 97.5 %
beta1 7.339277e+00 7.399593e+00
alpha1 6.977796e+00 7.164122e+00
N 9.098771e+03 1.136233e+04
I1 9.289270e-04 7.267604e-03
beta2 7.583730e+00 7.672804e+00
I2 6.422068e-04 6.109245e-03
r 2.576223e+02 3.864986e+02
So, r = 128.1481.
AICc value 352.8229
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).
Weston: I'm a bit concerned with the regional affect here. It appears that Ontario is the only one which peaks like the second SIR model.
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: Here, the first SIR model (red) corresponds to type B flu (green) very well and the second SIR model (yellow) corresponds to type A flu (blue).