Go back to Flu Mortality
Result for the “BFGS” method for the 1989-1990 epidemic (different alpha values):
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 = 1.481242e+01 alpha1 = 1.416913e+01 Ne = 3.848217e+03 I1 = 2.305288e-03 beta2 = 7.103694e+00 alpha2 = 6.282525e+00 I2 = 3.784437e-01
So, this implies that f = 3.848217e+03/27653146 = 0.0001391602
The MLE was -72.46
The confidence intervals for the coefficients
2.5 % 97.5 %
beta1 1.439883e+01 1.493666e+01
alpha1 1.408291e+01 1.443996e+01
N 4.404242e+03 4.795422e+03
I1 3.418788e-03 1.131072e-02
beta2 7.057222e+00 7.459279e+00
alpha2 5.974176e+00 6.489355e+00
I2 2.919702e-01 9.506168e-01
It switched to a Poisson distribution when r > 10,000.
AICc value 169.1047
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).
Weston: The Ontario data definitely has the same distinctive shape as the overall Canadian data and it's peaks do seem to be influencing the two SIR models heavily. However, it is seen that both BC and Quebec have two slight peaks at similar locations to the Ontario data. Since we do not have laboratory data for this early, I cannot plot the type A and B data to see how they look in comparison to the two SIR models. I will do the 1994-1995, 1995-1996, 1996-1997, 1997-1998, and 1998-1999 epidemics next because they have type A and B data. I'm also going to get rid of Poisson distribution entirely for all of these next epidemics and see what happens.