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Result 1997-1998 epidemic 3 SIR model Baseline Same Alpha BFGS (neg fast C code)
For the guess of parameters beta1 = 4.9 alpha1 = 4.8 Ne = 8551.444 I1 = 1 beta2 = 5.3 I2 = 1 beta3 = 4.9 I3 = 1, we obtained
beta1 = 3.374604e+00 alpha1 = 3.496639e+00 Ne = 8.550538e+03 I1 = 3.645167e+00 beta2 = 3.660098e+00 I2 = 1.526389e+00 beta3 = 3.996456e+00 I3 = 1.756606e-03
So, this implies that f = 8.550538e+03/30170983 = 0.0002834027
The MLE was -152.73
The confidence intervals for the coefficients
2.5 % 97.5 %
beta1 2.265152e+00 3.477191e+00
alpha1 3.470616e+00 4.327527e+00
N 2.020268e+04 2.071733e+04
I1 1.474458e+01 1.649570e+01
beta2 3.442959e+00 3.927080e+00
I2 4.766457e+00 4.776614e+00
beta3 3.532045e+00 4.090648e+00
I3 1.300450e-02 1.650161e-02
r 6.253368e+03 8.089292e+03
So, r = 832.6641
AICc value 330.13
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, brown is the third SIR model, and orange is the baseline)
Here are the three SIR models, overall data, and regional data (blue is the BC data, green is the Ontario data, and purple is the Quebec data).
Here are the three SIR models, overall data, and laboratory data (blue is the type A flu data, green is the type B flu data).