Let's consider the economic impact of the pandemic on the economy. Assume that the pandemic evolves according to the basic SIR model: S i R and = = = -BS(t)I(t) BS(t)I(t)-I(t) yI (t) with initial conditions S(0), I(0), and R(0), satisfying S(0)+1(0) +R(0) = 1 S+I+R=0= S(t) + I(t) +R(t) = 1 for all t > 0. Assume that some fraction 0 < < 1 of infected people are too sick to work. This implies that during the pandemic the effective labour force E(t) is given by (1) (2) (3) E(t) = (1 - I (t))L, where we assume the labour (I) is fixed and does change over time. Finally, assume that production is Cobb-Douglas such that Y(t) = K (AE(t))-a, where capital is fixed (K) and technology (A) are fixed. (a) Find an expression for the growth rate of output in terms of the growth rate of infections 91 = 1/1(t). Is output growth positively or negatively related to infection growth? (b) Let K = A = L = 1, a = 0.33, p = 0.5, S(0) = 1, and the solution path for infections be I(t) = 1- S(t) + In(S(t)/S(0)). Create a MATLAB graph that plots output against the percentage of the population that is susceptible. Compare Ro = 2.5 to Ro = 1.4, where the latter is the average Ro of seasonal influenza. Assuming o is the same for Covid and influenza, is Covid's impact on the economy similar to influenza in this model? (Tip: set the axes to go no higher than 1, e.g. axis ([0 1 0.5 1]) so that only values of I(t) >0 are shown.) Ro