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Result 1997-1998 epidemic 2 SIR model Baseline Different Alpha BFGS (neg fast C code)
For the guess of parameters beta1 = 1.1 alpha1 = 1 Ne = 8551.444 I1 = 1 beta2 = 1.1 alpha2 = 1 I2 = 1, we obtained
beta1 = 2.393558e+00 alpha1 = 2.265737e+00 Ne = 8.551053e+03 I1 = 4.315410e+00 beta2 = 4.386797e+00 alpha2 = 3.863950e+00 I2 = 9.347950e-04
So, this implies that f = 8.551053e+03/30170983 = 0.0002834198
The MLE was -153.25
The confidence intervals for the coefficients
2.5 % 97.5 %
beta1 2.366477e+00 2.415956e+00
alpha1 2.244217e+00 2.291977e+00
N 8.551017e+03 9.062057e+03
I1 3.153826e+00 5.821507e+00
beta2 4.375202e+00 4.397977e+00
alpha2 3.854827e+00 3.873042e+00
I2 1.098573e-02 1.259818e-02
r 6.959933e+03 9.081637e+03
So, r = 693.8942.
AICc value 327.6377
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: It's neat to be able to see which flu the SIR models correspond too. In this case, the first SIR model (red) corresponds to type B (green) and the second SIR model (yellow) corresponds to type A (blue).