Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)
6th Edition
ISBN: 9781524908102
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 12.8, Problem 20PS
To determine
To find the Jacobian
Where,
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The spread of an infectious disease is often modeled using the following autonomous differential equation:
dI
-
- BI(N − I) − MI,
dt
where I is the number of infected people, N is the total size of the population being modeled, ẞ is a constant determining the rate of
transmission, and μ is the rate at which people recover from infection.
Close
a) (5 points) Suppose ẞ = 0.01, N = 1000, and µ = 2. Find all equilibria.
b) (5 points) For the equilbria in part a), determine whether each is stable or unstable.
c) (3 points) Suppose ƒ(I) = d. Draw a phase plot of f against I. (You can use Wolfram Alpha or Desmos to plot the function, or draw the
dt
function by hand.) Identify the equilibria as stable or unstable in the graph.
d) (2 points) Explain the biological meaning of these equilibria being stable or unstable.
Find the indefinite integral.
Check
Answer:
7x
4 + 1x
dx
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Chapter 12 Solutions
Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)
Ch. 12.1 - Prob. 1PSCh. 12.1 - Prob. 2PSCh. 12.1 - Prob. 3PSCh. 12.1 - Prob. 4PSCh. 12.1 - Prob. 5PSCh. 12.1 - Prob. 6PSCh. 12.1 - Prob. 7PSCh. 12.1 - Prob. 8PSCh. 12.1 - Prob. 9PSCh. 12.1 - Prob. 10PS
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