1. Read this website about the The SIR Model fo Spread of Disease { The Di erential Equation Model: https://www.maa.org/press/periodicals/loci/joma/the-sir-model-for-spread -of-disease-the-differential-equation-model
Notice the gure at the bottom of the page showing the population trajectories. You’re going to reproduce that gure.
2. Implement Euler’s method for the SIR system. Find a stepsize h such that a plot of your Euler trajectories matches the website’s gure. What value did you get for h, and how did you get it ?
3. Repeat the previous problem with Runge-Kutta 2.
4. BONUS (20 points): Repeat the previous problem with Runge-Kutta 4.
5. BONUS (50 points): Design and run a convergence study with respect to h for both Runge-Kutta 2 and 4. Choose the range of h’s informed by (i) the values you found in problems 3 and 4 and (ii) a goal to determine the asymptotic regime for RK2/4 applied to the SIR system. (This is such a good problem. This is the kind of problem you talk about in a job interview to demonstrate your deep knowledge of the subject.)
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