The Kermack-McKendrick equations from Exercise 23 can be extended to model persistent diseases rather than single outbreaks by including an inflow of susceptible individuals and their natural death. This gives the differential equations S9 −  2 S 2 SI I9 − SI 2 I where  and  are positive constants representing inflow and mortality of susceptible individuals, respectively.

(a) Suppose  − 1,  − 1,  − 1, and  − 10. Construct the phase plane including all nullclines, equilibria, and arrows indicating the direction of movement in the plane.

(b) Suppose  − 1 15,  − 1,  − 1, and  − 10. Construct the phase plane including all nullclines, equilibria, and arrows indicating the direction of movement in the plane.

(c) What is the difference in the predicted dynamics between part

(a) and part (b)?