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Result for the “BFGS” method for the 1989-1990 epidemic (6 parameters, alpha values are the same for both the models):
For the guess of parameters beta1 = 0.3 alpha = 0.2 Ne = 1377 I1 = 1 beta2 = 0.3 I2 = 1, we obtained
beta1 = 2.9606888 alpha = 2.0481982 Ne = 1376.3008121 I1 = 0.6220539 beta2 = 2.4900060 I2 = 0.3145368
So, this implies that f = 1376.3008121/27653146 = 0.00004977
The covariance matrix was
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] -0.0084830777 -0.009578108 -6.261064 -0.001202157 -9.240969e-03 7.411367e-04 [2,] -0.0095781084 -0.009506844 -5.643501 0.002233492 -9.413388e-03 1.569764e-03 [3,] -6.2610642616 -5.643500874 -994.159681 3.312879549 -6.272385e+00 2.846079e+00 [4,] -0.0012021566 0.002233492 3.312880 0.012409315 1.755700e-03 1.736288e-03 [5,] -0.0092409687 -0.009413388 -6.272385 0.001755700 -8.667328e-03 -9.570228e-05 [6,] 0.0007411367 0.001569764 2.846079 0.001736288 -9.570228e-05 5.693951e-03
The MLE was 4041.036
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)