Let S and I satisfy the differential equations in Problem 1. Assume I ≠ 0.

Data from in problem 1

(a) If dI∕dt = 0, find S.
(b) Show that I increases if S is greater than the value you found in part (a). Show that I decreases if S is less than the value you found in part (a).
(c) Explain how you know that your answer to part (a) is the threshold value.

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 = -ASI = aSI - bI where a, b are positive constants. dt