Show that if S, I, and R satisfy the differential equations in Problem 1, the total population, S + I + R, is constant.

Data from in problem 1

Let I be the number of infected people and S be the number of susceptible people in an outbreak of a dis- ease. Explain why it is reasonable to model the interac- tion between these two groups by the differential equa- tions dS dt dI dt = -aSI =aSI-bl where a, b are positive constants.