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.

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.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 18T

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