In tracking the propagation of a disease, a population can be divided into 3 groups: the...

 

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In tracking the propagation of a disease, a population can be divided into 3 groups: the portion that is susceptible, S(t), the portion that is infected, F(t), and the portion that is recovering, R(t). Each of these will change according to a differential equation: S' = F = -5 R' = so that the portion of the population that is infected is increasing in proportion to the number of susceptible people that contract the disease, and decreasing as a proportion of the infected people who recover. If we introduce the vector y = [S F R, this can be written in matrix form as y' = Ay. If one of the solutions is y = x1 + 600 e-ud x, + 500 e-t/c X3 , where x1 = [0 0 50,000], x2 = [0 -1 1]', and x3 [b 63 -81]", what are the values of a, b, and c? %3D In tracking the propagation of a disease, a population can be divided into 3 groups: the portion that is susceptible, S(t), the portion that is infected, F(t), and the portion that is recovering, R(t). Each of these will change according to a differential equation: S' = F = -5 R' = so that the portion of the population that is infected is increasing in proportion to the number of susceptible people that contract the disease, and decreasing as a proportion of the infected people who recover. If we introduce the vector y = [S F R, this can be written in matrix form as y' = Ay. If one of the solutions is y = x1 + 600 e-ud x, + 500 e-t/c X3 , where x1 = [0 0 50,000], x2 = [0 -1 1]', and x3 [b 63 -81]", what are the values of a, b, and c? %3D

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4 o 0 4 4 0 O 1 0 2 R 3D A 63 ta X x 600 ... View the full answer