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The data I'm using for our epidemic

data2 = c(0.8760308, 14.6437410, 28.4196368, 47.2210290, 73.0648590, 136.9674535, 166.9442884, 163.0097641, 125.1769971, 70.4576305, 44.8616645, 71.3973124, 34.0708812, 76.8866802, 36.8469589, 36.9518742, 22.1994882, 27.5857962, 4.1047848)

t2 = c(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18)

and this is the practice data

data = c(3, 6, 25, 73, 222, 294, 258, 237, 191, 125, 69, 27, 11, 4)

t = c(1:14)

Results for the test data:

For the guess of parameters beta = 0.3, alpha = 0.2, N = 1800, and I0 = 1 on the simple data, we obtained

beta = 1.7115563 alpha = 0.7575198 Ne = 1799.0605934 I0 = 1.8465230

The covariance matrix was

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

[1,] 0.00779983 0.007606950 2.935721 -0.010735336 [2,] 0.00760695 0.009084120 6.435114 0.007759467 [3,] 2.93572053 6.435113708 11376.028419 38.639409279 [4,] -0.01073534 0.007759467 38.639409 0.228431946

The MLE was 6448.757

Here’s a plot of the model with the data (blue is the model and red is the data)

simple_sir_graph_and_model_red_data_blue_is_the_new_model_.pdf