Let S and I satisfy the differential equations in Problem 1. Assume I 0. Data from

Question:

Let S and I satisfy the differential equations in Problem 1. Assume I ≠ 0.

Data from in problem 1

(a) If dI∕dt = 0, find S.
(b) Show that I increases if S is greater than the value you found in part (a). Show that I decreases if S is less than the value you found in part (a).
(c) Explain how you know that your answer to part (a) is the threshold value.

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Applied Calculus

ISBN: 9781119275565

6th Edition

Authors: Deborah Hughes Hallett, Patti Frazer Lock, Andrew M. Gleason, Daniel E. Flath, Sheldon P. Gordon, David O. Lomen, David Lovelock, William G. McCallum, Brad G. Osgood, Andrew Pasquale

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Question Posted: Apr 11, 2023 02:10 AM

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Let S and I satisfy the differential equations in Problem 1. Assume I 0. Data from

Question:

Let I be the number of infected people and S be the number of susceptible people in an outbreak of a dis- ease. Explain why it is reasonable to model the interac- tion between these two groups by the differential equa- tions ds dt dI = -ASI = aSI - bI where a, b are positive constants. dt

Step by Step Answer:

a Setting dIdt 0 b For S ba we know ...View the full answer

Applied Calculus

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