2. Consider the following SIR model for an epidemic dS = -BSI, dt dI = BSI-I, dt dR = , dt where S(t) is the number of susceptible people, I(t) is the number of people infected, and R(t) is the number of people who have recovered. In this model, is a parameter depending on the transmission (infection) rate of the disease and y is a parameter depending on the recovery rate. For this problem, assume that = 0.7 and y = 0.3, and the initial conditions S(t = 0) = 0.99, I(t = 0) = 0.01, and R(t = 0) = 0. == (a) Some people think that the number of infected people should have passed its peak by the time we reach t = 10. What do you think? (b) At the end of the epidemic, what percentage of the population would have gotten the disease and recovered? (c) If we practice good measures such as social distancing, wearing face coverings, and frequent hand-washing to lower the transmission rate such that we have a lower = 0.4, what will be the new answer to part (b)?