5. The Spread of a Contagious Disease. Consider the following ordinary differential equation model for the spread of a communicable disease: dN 0.25N(10 – N), N(0) = 2 %3D dt (a) where N is measured in 100's. Analyze the behavior of this differential equation as follows. a. Since this is an autonomous differential equation, perform a qualitative graphical analysis as discussed in Section 11.4. (i) Plot dN/dt versus N. Find and label all rest points (equilibrium points). (ii) Estimate the value where the rate of change of the disease is the fastest. Justify your answer. (iii) Plot N versus t for each of the following initial conditions: N (0) = 2, N(0) = 7, and N(0) 14. %3D
5. The Spread of a Contagious Disease. Consider the following ordinary differential equation model for the spread of a communicable disease: dN 0.25N(10 – N), N(0) = 2 %3D dt (a) where N is measured in 100's. Analyze the behavior of this differential equation as follows. a. Since this is an autonomous differential equation, perform a qualitative graphical analysis as discussed in Section 11.4. (i) Plot dN/dt versus N. Find and label all rest points (equilibrium points). (ii) Estimate the value where the rate of change of the disease is the fastest. Justify your answer. (iii) Plot N versus t for each of the following initial conditions: N (0) = 2, N(0) = 7, and N(0) 14. %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:5. The Spread of a Contagious Disease. Consider the following ordinary differential
equation model for the spread of a communicable disease:
dN
0.25N(10 – N), N (0) = 2
(a)
dt
where N is measured in 100's. Analyze the behavior of this differential equation as
follows.
a. Since this is an autonomous differential equation, perform a qualitative graphical
analysis as discussed in Section 11.4.
(i) Plot dN/dt versus N. Find and label all rest points (equilibrium points).
(ii) Estimate the value where the rate of change of the disease is the fastest. Justify
your answer.
(iii) Plot N versus t for each of the following initial conditions:
N(0) = 2, N(0) = 7, and N(0) = 14.
%3D
(iv) Describe the stability of each rest point (equilibrium point).
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