The Kermack-McKendrick equations from Exercise 23 can be extended to model persistent
Chapter 7, Problem 24(choose chapter or problem)
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)?
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