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Differential Equations Solutions 99

Differential Equations Solutions 99 - ν = 0 0.1 0.2 and...

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Chapter 19 Solutions: Case Study: Models of Infection: Person to Person CHALLENGE 19.1. See the solution to Challenge 3. CHALLENGE 19.2. See the solution to Challenge 3. CHALLENGE 19.3. The results of a simulation of each of these three models are given in Figures 19.1-19.3. The MATLAB program that generated these results can be found on the website. In general, mobility increases the infection rate and vaccination decreases it dramatically. In our sample runs, the infection peaks around day 18 with no mobility, and around day 15 when patients are moved. Individual runs may vary. CHALLENGE 19.4. The histograms for
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Unformatted text preview: ν = 0, 0.1, 0.2, and 0.3 are shown in Figure 19.4. The mean percent of the population infected drops from 73 . 6% for ν = 0 (with a variance of 4 . 5%), to 4 . 1% for ν = 0 . 3 (with a variance of only 0 . 06%). CHALLENGE 19.5. From Challenge 4, we know that a very low vaccination rate is sufficient to dramatically reduce the infection rate: somewhat less than ν = 0 . 1. But using a nonlinear equation solver on a noisy function is quite dangerous; it is easily fooled by outliers, and by changing the starting guess, you can make it produce almost any value. 109...
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