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Result 1991-1992 epidemic 3 SIR model Baseline Same Alpha BFGS (neg fast C code)
For the guess of parameters beta1 = 2.3 alpha1 = 2.2 Ne = 4275.722 I1 = 1 beta2 = 2.3 I2 = 1 beta3 = 2.3 I3 = 1, we obtained
beta1 = 1.129149e+01 alpha1 = 1.086239e+01 Ne = 4.276004e+03 I1 = 4.108273e-03 beta2 = 1.164320e+01 I2 = 3.634489e-03 beta3 = 1.111417e+01 I3 = 1.002055e+00
So, this implies that f = 4.276004e+03/28301730 = 0.0001510863
The MLE was -82.09
Weston: This CI contains a NA value.
The confidence intervals for the coefficients
2.5 % 97.5 %
beta1 1.076649e+01 1.142229e+01
alpha1 1.077900e+01 1.135883e+01
N 4.955968e+03 5.446927e+03
I1 8.932846e-03 1.043779e-01
beta2 1.073215e+01 1.175746e+01
I2 1.140638e-03 NA
beta3 9.134223e+00 1.155060e+01
I3 2.032744e+00 2.490658e+00
r 8.212042e+09 9.400840e+09
So, r = 17,997,748.
AICc value 196.0226
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).