Go back to Flu Mortality
Result for the “BFGS” method for the 1989-1990 epidemic (different alpha values and only negative binomial distribution):
For the guess of parameters beta1 = 0.3 alpha1 = 0.2 Ne = 3876.95 I1 = 1 beta2 = 0.3 alpha2 = 0.2 I2 = 1, we obtained
beta1 = 2.149584e+01 alpha1 = 2.085659e+01 Ne = 5.641608e+03 I1 = 1.697683e-03 beta2 = 1.051405e+01 alpha2 = 9.699624e+00 I2 = 2.608408e-01 r = 1.356627e+06
Weston: I was hoping that these values would be very close to the ones obtained in the previous Poisson model, but they are significantly different from looking at the confidence intervals given.
So, this implies that f = 5.641608e+03/27653146 = 0.0002040132
The MLE was -72.41
The confidence intervals for the coefficients
2.5 % 97.5 %
beta1 2.107035e+01 2.158733e+01
alpha1 2.076600e+01 2.123519e+01
N 4.904939e+03 6.106561e+03
I1 2.542968e-03 7.967457e-03
beta2 1.047815e+01 1.081218e+01
alpha2 9.401475e+00 9.735949e+00
I2 2.141102e-01 6.474933e-01
r 2.443650e+08 2.796208e+08
The r value is 1356627.
AICc value 175.2287
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).