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Unformatted text preview: d , r and γ . Group all terms by variable . 2. Simplify the model by assuming constant population N . Note that this allows you to eliminate variables as follows: (a) Since births must match deaths, d = b . (b) Since total population is constant, R = N-S-I . You should end up with two equations in the variables S and I . You also have a new parameter, N . Group by variable . 1 3. Assume constant values b = 0 . 02, r = 0 . 01, γ = 0 . 1 and N = 100. Perform the usual analysis. That is: (a) Think about what happens if S = 0. Sketch solutions if you can. (b) Think about what happens if I = 0. Sketch solutions if you can. (c) Find all equilibria. (d) For each equilibrium, ±nd eigenvalues, ±nd eigenvectors, and sketch solutions. 2...
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- Fall '08
- Math, Expression, Assume constant values