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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

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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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