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Result for the “BFGS” method for the 1989-1990 epidemic with the triple SIR model (different alpha values, mle2, Neg Bin/Poi log-lik):

For the guess of parameters beta1 = 0.3 alpha1 = 0.2 Ne = 1377 I1 = 1 beta2 = 0.3 alpha2 = 0.2 I2 = 1 beta3 = 0.3 alpha3 = 0.2 I3 = 1, we obtained

beta1 = 2.881849e+00 alpha1 = 1.946970e+00 Ne = 1.376856e+03 I1 = 4.652498e-01 beta2 = 2.390684e+00 alpha2 = 2.328340e+00 I2 = 3.002232e+00 beta3 = 5.624027e+00 alpha3 = 4.984448e+00 I3 = 6.046721e-03

So, this implies that f = 1.376856e+03/27653146 = 4.979021e-05

The MLE was -72.56

AICc = 192.6293

A Poisson log-likelihood function was chosen because the negative binomial parameter r was greater than 1000.

Here’s a plot of the model with the data (red is the data, blue is the sum of the two models, purple is the lamb1 model, green is the lamb2 model, brown is the lamb3 model, and orange is the baseline)

1989-1990_epi_3_model_base_mle2_neg_or_poi.pdf