Consider the scenario from the problem above. Let's suppose we are now dealing with aninfectious disease that is transmittable via contact with an infected person. As before, define:S number of the people in the population who are susceptible.I= number of the people in the population who are infectedt = time since outbreak observed, daysHowever, let's assume the following:Each day, .4% of people who are susceptible become infected and 4% of infected people become immune.Each infected person will infect 3 susceptible people per day. Some people who are infected do not becomeimmune, but instead are once again susceptible to getting the disease again-suppose this is 7% of allinfected people. Finally, each day 2% of people who are susceptible take a vaccine and so become immune.Remember that all people who are immune are out of the picture of our model.NOTE: You will not be solving this system of differential equations!a) Draw a diagram similar to that of our "tank" problems that shows the transition rates between thetwo groups. Though we are not dealing with water and chemicals, we can still think about the "flows"in an analogous way.b.) Write a system of differential equation forsusceptibles and infecteds.to model the rate of change of the number ofc.) Find any equilibrium point(s) of this system. Explain what this point(s) mean in the context of theproblem. If applicable, you can round to two decimal places (e.g. 213.135 rounds to 213.14).d.) Classify the equilibrium point(s). What does this say about the long-run nature of this disease forthe two groups considered?

As per the question, we are tasked with modeling the spread of an infectious disease within a…

a) Draw a diagram similar to that of our "tank" problems that shows the transition rates between the two groups. Though we are not dealing with water and chemicals, we can still think about the "flows" in an analogous way. b) Write a system of differential equation for .. susceptibles and infecteds. to model the rate of change of the number of c.) Find any equilibrium point(s) of this system. Explain what this point(s) mean in the context of the problem. If applicable, you can round to two decimal places (e.g. 213.135 rounds to 213.14).

a) Draw a diagram similar to that of our "tank" problems that shows the transition rates between the two groups. Though we are not dealing with water and chemicals, we can still think about the "flows" in an analogous way. b) Write a system of differential equation for .. susceptibles and infecteds. to model the rate of change of the number of c.) Find any equilibrium point(s) of this system. Explain what this point(s) mean in the context of the problem. If applicable, you can round to two decimal places (e.g. 213.135 rounds to 213.14).

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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Question

Consider the scenario from the problem above. Let's suppose we are now dealing with an
infectious disease that is transmittable via contact with an infected person. As before, define:
S number of the people in the population who are susceptible.
I= number of the people in the population who are infected
t = time since outbreak observed, days
However, let's assume the following:
Each day, .4% of people who are susceptible become infected and 4% of infected people become immune.
Each infected person will infect 3 susceptible people per day. Some people who are infected do not become
immune, but instead are once again susceptible to getting the disease again-suppose this is 7% of all
infected people. Finally, each day 2% of people who are susceptible take a vaccine and so become immune.
Remember that all people who are immune are out of the picture of our model.
NOTE: You will not be solving this system of differential equations!
a) Draw a diagram similar to that of our "tank" problems that shows the transition rates between the
two groups. Though we are not dealing with water and chemicals, we can still think about the "flows"
in an analogous way.
b.) Write a system of differential equation for
susceptibles and infecteds.
to model the rate of change of the number of
c.) Find any equilibrium point(s) of this system. Explain what this point(s) mean in the context of the
problem. If applicable, you can round to two decimal places (e.g. 213.135 rounds to 213.14).
d.) Classify the equilibrium point(s). What does this say about the long-run nature of this disease for
the two groups considered?

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