The SIR model for modeling infectious diseases is given by \left\{\begin{array}{l} S^{\prime}(t)=-\frac{\beta}{N} I(t) S(t) \\ I^{\prime}(t)=\frac{\beta}{N} I(t) S(t)-\gamma I(t) \\ R^{\prime}(t)=\gamma I(t) \end{array}\right. where N is the total number of people in a given population, S(t) is the number of susceptible people attime t, I(t) is the number of infected people at time t, R(t) is the number of removed people at time t,and 3,y quantify rates of spread and removal. 1. Given the parameters 3 = 3, y = .2, use Euler's method with Ax = .1 to solve the SIR model withinitial conditions S(0) = 9997, I(0) = 3, R(0) = 0 for 0 <t < 20. 2. Given the parameters 3 = 1, y = .2, us Euler's method with Ax = .1 to solve the SIR model withinitial conditions S(0) = 9997, I(0) = 3, R(0) = 0 for 0 < t< 20. 3. Given the parameters 3 = 1,7 = .8, us Euler's method with Ax = .1 to solve the SIR model withinitial conditions S(0) = 9997, I(0) = 3, R(0) = 0 for 0 < t < 20. Your final excel file should have plots for all three scenarios above. Discuss the differences between thefound for the different values of the parameters and how this is related to infectious diseasesolutionsyoumodeling.

Question

The SIR model for modeling infectious diseases is given by \left\{\begin{array}{l} S^{\prime}(t)=-\frac{\beta}{N} I(t) S(t) \\ I^{\prime}(t)=\frac{\beta}{N} I(t) S(t)-\gamma I(t) \\ R^{\prime}(t)=\gamma I(t) \end{array}\right. where N is the total number of

people in a given population, S(t) is the number of susceptible people attime t, I(t) is the number of infected people at time t, R(t) is the number of removed people at time t,and 3,y quantify rates of spread and removal. 1. Given the parameters 3 = 3, y = .2, use Euler's method with Ax = .1 to solve the SIR model withinitial conditions S(0) = 9997, I(0) = 3, R(0) = 0 for 0