The goal of this problem is to use the solution of the SIR model below to find the parameters of an infectious disease. S =SI, (1) I =SII, R = I . Suppose an epidemic breaks out and the following data is collected during the epidemic Susceptible Infected 250 6 230 14 200 20 150 25 120 20 100 8 90 8 80 0. (a) Write down the equation which relates S with I. (This can be found in the notes, simply copy it from there) From the table above plug into this equation the initial and the final values for S and I. From the resulting ex- pression find the value of the ratio between the recovery rate and the infection rate . (b) Suppose we know that the duration of the infectious period is 10 days. Using this, and part (a) find the infection rate . Hint: Recall that the re- ciprocal of the death rate gives you the expected life-time of an individual. The same concept works here if we replace "life-time" with "duration of the infectious period" (c) Use the NonlinearFit command in Maple to estimate the value of that you found above as follows: From the equation that relates I with S, write I as a function of S (keep I on the left hand side). Make sure you replace S0, I0 and with their corresponding value. When this is done, I should be a function of S with only one parameter: . Enter the S coordinates in the X- vector and I coordinates in the Y-vector. Then use NonlinearFit command with this function (look at the template from WEEK 5). If successful you should see the estimated value for given by Maple which should be close to the one you found in part (b)