An athlete infected with the mumps returned to college at Syracuse University in August of 2017. The campus has a student population of 7500 students that live on campus. The rate at which the mumps spread is proportional not only to the number of infected students but also to the number of students not yet infected. By November of 2017, there were 37 students infected.

(a) If no interventions were taken, how long would it have taken for half the student population living on campus to be infected?

(b) The health clinic began offering vaccine to students, suppose that each month starting in November, 1000 students received the vaccination. How would your answer to part (a) be effected?

(c) Students that received the vaccination were still getting mumps. It turns out that the vaccination was only 75% effective when one dose is administered. How does this fact change your answer to part (b)?