Go back to Flu Mortality
Result for the “BFGS” method for the 1989-1900 epidemic:
For the guess of parameters beta1 = 0.3 alpha1 = 0.2 Ne = 1377 I1 = 1 beta2 = 0.3 alpha2 = 0.2 I2 = 1, we obtained
beta1 = 5.280657e+00 alpha1 = 4.651532e+00 Ne = 1.376953e+03 I1 = 6.976663e-03 beta2 = 2.261040e+00 alpha2 = 1.417738e+00 I2 = 1.179858e+00
So, this implies that f = 1376.953/27653146 = 0.000049793
The covariance matrix was
[,1] [,2] [,3] [,4]
[1,] 0.474722028 0.465547432 4.287726e+01 -1.941503e-03 [2,] 0.465547432 0.457593268 4.337841e+01 -1.828452e-03 [3,] 42.877259755 43.378409548 1.215924e+04 -2.168046e-02 [4,] -0.001941503 -0.001828452 -2.168046e-02 1.491067e-05 [5,] 0.013010215 0.013807399 1.859597e+01 2.046499e-04 [6,] 0.026089296 0.027021407 1.998082e+01 1.710319e-04 [7,] 0.065642987 0.065929939 -1.574266e+00 -2.860954e-04
[,5] [,6] [,7]
[1,] 0.0130102146 0.0260892959 0.0656429868 [2,] 0.0138073989 0.0270214069 0.0659299386 [3,] 18.5959718481 19.9808204217 -1.5742656729 [4,] 0.0002046499 0.0001710319 -0.0002860954 [5,] 0.0631796289 0.0596675018 -0.0558128983 [6,] 0.0596675018 0.0577938310 -0.0446388989 [7,] -0.0558128983 -0.0446388989 0.1025670873
The MLE was 4045.962
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)