Go back to Flu Mortality
Result 1996-1997 epidemic 3 SIR model Baseline Same Alpha BFGS (neg fast C code)
For the guess of parameters beta1 = 7.4 alpha1 = 7 Ne = 7918.306 I1 = 1 beta2 = 7.6 I2 = 1 beta3 = 7.01 I3 = 1, we obtained
beta1 = 7.702796e+00 alpha1 = 7.626431e+00 Ne = 7.918192e+03 I1 = 2.105590e+00 beta2 = 8.322980e+00 I2 = 5.546439e-04 beta3 = 7.984736e+00 I3 = 1.710007e-03
So, this implies that f = 7.918192e+03/29888998 = 0.0002649200
The MLE was -159.15
The confidence intervals for the coefficients
2.5 % 97.5 %
beta1 7.594289e+00 7.781202e+00
alpha1 7.613170e+00 7.637428e+00
N 8.809479e+03 8.630812e+03
I1 3.867498e+00 4.407035e+00
beta2 8.309476e+00 8.338833e+00
I2 3.809212e-04 1.327854e-03
beta3 7.968152e+00 8.002452e+00
I3 1.019019e-03 2.326720e-03
r 1.046781e+03 1.571993e+03
So, r = 295.6477
AICc value 342.7335
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).