The Kermack-McKendrick equations are first-order differential equations describing an

Chapter 7, Problem 23

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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.

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