Recall that the SIR system of differential equations that we discussed in class was as follows:

dS

dt = S I

dI

dt = S I

I

5

dR

dt =

I

5

1. Explain why dI

dt is a combination of the terms from dS

dt and dR

dt in the original system.

2. How would this system of equations change if people stayed infected for 9 days? Write

three equations.

3. How would the original system of equations change if only 30 % of interactions with an infected

person caused an infection? Again, write three equations.