Answer Happy

3. In this exercise, we will use iteration (as in Ex. 3 of the Module 2 spreadsheet tutorial] to calculate solutions by iteration for the SIR epidemic model St+1 = St - bStiti It+1 = 1 + b Silt - kli, Rt+1 = Rt + klt So = 5,230, 330 lo = 8,000 Ro = 0 and explore the effect of changing the value of parameter k. Here t is measured in days. (a) Put the parameters b=0.000000075 and k = 0.11 at the top of a new worksheet and label them. (b) Use a spreadsheet formula to tabulate values of t from 0 to 150 in the first column and include a column label. (c) Use the method of Exercise 3 of the module 2 spreadsheet tutorial to calculate the values of St. l4 and Rt from t=0 to t = 150 by iteration (and include column labels). As always, use '$-signs' for the parameter entries your formulas. It is easiest to drag down the formulas for all three columns at once. (d) Create a fourth column using appropriate cell formulas to calculate the total population Seth + Re at each time t and label this column N. The values in this column should always be the same. If they are not, you ha made a mistake and ould check your work. (e) Create an "x-y plot" of the solution columns for St, I and Rt. You should see an epidemic where the number of infectives peaks at 29 days. (f) In another cell in your table calculate the herd immunity for this model (and label it). (g) Use trial and error to adjust the recovery parameter k so that the herd immunity is as close to 0.95*N as possible. Restrict your value of k to 5 decimal places. Leave k set to this value for your submission.