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Result for the “BFGS” method for the 1989-1990 epidemic (different alpha values, mle2, three SIR model):

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 = 2.348711e+00 alpha1 = 1.482033e+00 Ne = 1.376895e+03 I1 = 9.520094e-01 beta2 = 5.022865e+00 alpha2 = 4.399454e+00 I2 = 7.847178e-03 beta3 = -3.222657e-02 alpha3 = -2.259459e-01 I3 = 1.543590e+00

So, this implies that f = 1.376895e+03/27653146 = 4.979162e-05

The MLE was -72.85

AICc = 193.2097

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_base_mle2_3_mod.pdf

Weston: This model gave just as good a fit as the two SIR model. The AICc is larger and the third SIR model is not useful, having negative beta and alpha values. Hence, the two SIR model is better for this epidemic.