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Result for the “BFGS” method with 1992-1993 epidemic data (6 parameters, same alpha values):

For the guess of parameters beta1 = 0.3 alpha = 0.2 Ne = 1434 I1 = 1 beta2 = 0.3 I2 = 1, we obtained

beta1 = 1.5064868 alpha = 1.1904065 Ne = 1434.0585717 I1 = 0.1318584 beta2 = 1.2297169 I2 = 7.9884115

So, this implies that f = 1434.0585717/27653146 = 0.000051859

The covariance matrix was

            [,1]          [,2]          [,3]         [,4]          [,5]

[1,] -0.59138870 -0.60867119 -613.39852 0.012037218 -0.59875233 [2,] -0.60867119 -0.62560911 -626.21628 0.014448713 -0.61597647 [3,] -613.39852231 -626.21627661 -599553.21137 25.577321807 -620.61512442 [4,] 0.01203722 0.01444871 25.57732 0.005017718 0.01260903 [5,] -0.59875233 -0.61597647 -620.61512 0.012609029 -0.60556181 [6,] 3.93369290 4.05078073 4137.43114 -0.067715886 3.96114392

            [,6]

[1,] 3.93369290 [2,] 4.05078073 [3,] 4137.43114478 [4,] -0.06771589 [5,] 3.96114392 [6,] -24.70836017 [1] 1853.350

The MLE was 1853.350

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)

two_sir_bfgs_6_param_alpha_same_1992-1993_epi.pdf

Weston: Oddly enough, the model for this is really poor.