The Kermack-McKendrick equations are first-order differential equations describing an infectious disease outbreak. Using S and I to denote the number of susceptible and infected people in a population, the equations are S9 − 2SI I9 − SI 2 I where  and  are positive constants representing the transmission rate and rate of recovery, respectively.

(a) Provide a biological explanation for each term of the equations.

(b) Suppose  − 1 and  − 5. Construct the phase plane including all nullclines, equilibria, and arrows indicating the direction of movement in the plane.

(c) Construct the phase plane for arbitrary values of  and

, including all nullclines, equilibria, and arrows indicating direction of movement in the plane.