ws25 - do the following(a Linearize and ±nd eigenvalues(b...

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Math 464, Worksheet 25 In the SIR model from Worksheet 24 we assumed a constant probability of infection. This does not make sense; it should vary with the number of infected people. (Equivalently, with the fraction of the population that is infected.) From now on we will assume that r = βI/N for some positive constant β . 1. Make the substitution r = 0 . 06 I/N in your model from Worksheet 24. 2. Find all equilibrium solutions. 3. For each equilibrium in the region of positive solutions
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Unformatted text preview: do the following: (a) Linearize and ±nd eigenvalues. (b) For real eigenvalues, ±nd eigenvectors. (c) For complex eigenvalues, compute | λ + 1 | . (Recall that this tells you whether solutions spiral in or not.) 4. Use all this information to sketch a general picture of the possible solution curves for this model. Note: This is called a phase portrait . 5. Repeat Problems 1-4 for β = 0 . 12. 6. Repeat Problems 1-4 for β = 0 . 24. 1...
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