Go back to Flu Mortality
Result 1992-1993 epidemic 2 SIR model Baseline Same Alpha BFGS (neg fast C code)
For the guess of parameters beta1 = 4 alpha1 = 2.5 Ne = 4701.312 I1 = 1 beta2 = 1.2 I2 = 1, we obtained
beta1 = 7.370156e+00 alpha1 = 7.038650e+00 Ne = 4.701552e+03 I1 = 3.399253e+00 beta2 = 7.661509e+00 I2 = 4.270480e-03
So, this implies that f = 4.701552e+03/28680833 = 0.0001639266
The MLE was -93.4
The confidence intervals for the coefficients
2.5 % 97.5 %
beta1 6.618599e+00 7.446567e+00
alpha1 6.946868e+00 7.623735e+00
N 5.267882e+03 8.357866e+03
I1 2.087751e+00 5.860196e+00
beta2 6.771156e+00 7.766499e+00
I2 8.665545e-04 1.773578e-02
r 1.917642e+10 2.195537e+10
So, r = 21,903,928.
AICc value 207.8083
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).