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Result 1995-1996 epidemic 3 SIR model Baseline Same Alpha BFGS (neg fast C code)
For the guess of parameters beta1 = 1.5 alpha1 = 1.3 Ne = 5695.91 I1 = 1 beta2 = 4.8 I2 = 1 beta3 = 1.4 I3 = 1, we obtained
beta1 = 8.582693e+00 alpha1 = 8.546961e+00 Ne = 5.701510e+03 I1 = 2.066938e+00 beta2 = 8.905540e+00 I2 = 3.266929e-03 beta3 = 9.027820e+00 I3 = 5.416586e-02
So, this implies that f = 5.701510e+03/29598699 = 0.0001926270
The MLE was -122.16
The confidence intervals for the coefficients
2.5 % 97.5 %
beta1 5.346188e+00 8.905363e+00
alpha1 8.468489e+00 8.790022e+00
N 6.668542e+03 9.260570e+03
I1 3.946690e+00 4.835134e+00
beta2 8.461525e+00 8.980800e+00
I2 5.480467e-03 4.108368e-02
beta3 8.255842e+00 9.322173e+00
I3 1.674409e-02 5.473030e-01
r 1.826897e+08 2.091386e+08
So, r = 385,344.3
AICc value 270.8821
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).