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Result for the “BFGS” method for the 1989-1990 epidemic (5 parameters, alpha values are equal to 1/7 for both the models):
Weston: Setting the alpha values to 1/7, is not correct. Perhaps I'll try again with them equal to around one.
For the guess of parameters beta1 = 0.3 Ne = 1377 I1 = 1 beta2 = 0.3 I2 = 1, we obtained
beta1 = 0.3119233 Ne = 1146.8615307 I1 = 4.0274121 beta2 = 0.7378440 I2 = 10.9647797
So, this implies that f = 1146.8615307/27653146 = 0.00004147309
The covariance matrix was
[,1] [,2] [,3] [,4] [,5]
[1,] 8.229108e-04 -0.0001365216 -0.063265298 6.507124e-05 -0.002995546 [2,] -1.365216e-04 -0.9551443153 0.030190859 4.924638e-04 -0.035797595 [3,] -6.326530e-02 0.0301908588 5.682782704 9.745016e-03 -0.517095458 [4,] 6.507124e-05 0.0004924638 0.009745016 7.720312e-04 -0.047579524 [5,] -2.995546e-03 -0.0357975946 -0.517095458 -4.757952e-02 3.450704600
The MLE was 3996.859
Here’s a plot of the model with the data (red is the data, blue is the sum of the two models, green is the lamb2 model, and purple is the lamb1 model)
Weston: This does not give a good model.
Junling: Yes, but that means the infectious period is 7 weeks, that cannot be right. You might want to set it to 5/7 or 1.