Go back to Flu Mortality
Result 1990-1991 epidemic 3 SIR model Baseline Different Alpha BFGS (neg fast C code)
For the guess of parameters beta1 = 67.9 alpha1 = 66.6 Ne = 3838.472 I1 = 1 beta2 = 4.4 alpha2 = 4.1 I2 = 1 beta3 = 1.1 alpha3 = 1 I3 = 1, we obtained
beta1 = 6.718272e+01 alpha1 = 6.589521e+01 Ne = 3.838470e+03 I1 = 8.563926e-02 beta2 = 4.769621e+00 alpha2 = 4.461866e+00 I2 = 1.367022e+00 beta3 = 4.083520e-01 alpha3 = 9.632655e-04 I3 = 1.440856e-03
So, this implies that f = 3.838470e+03/28023630 = 0.0001369726
The MLE was -82.05
The confidence intervals for the coefficients
2.5 % 97.5 %
beta1 6.685849e+01 6.748021e+01
alpha1 6.559981e+01 6.621863e+01
N 5.439455e+03 5.678654e+03
I1 1.744332e-01 2.014249e-01
beta2 4.723951e+00 4.813253e+00
alpha2 4.418995e+00 4.507091e+00
I2 9.197917e-01 1.988935e+00
beta3 4.032866e-01 4.284223e-01
alpha3 3.817488e-01 4.912456e-01
I3 1.244726e-02 1.332300e-02
r 8.186147e+11 9.373168e+11
So, r = 435,063,138.
AICc value 210.1084
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).