Suppose we are modeling the spread of a disease. People are categorized as either susceptibleor infectious (similar to our Module 7 discussion board). Those who are susceptible do not have the disease,but could get it. Those who are infected currently have the disease. We assume this disease is nottransmittable by contact with an infectious person. Instead, we will assume it is something that is contractedthrough environmental factors.Define:dt= -.035.S= .03S - .021where.S = number of the people in the population who are susceptibleI= number of the people in the population who are infectedt = time since outbreak observed, daysNOTE: Here we are dealing with the number of people, rather than the proportion of people, in each group.This fact should not change your analysis in any significant way.Anyone who is not susceptible or infected falls into a third category: immune. We do not concern ourselveswith this group, because they are people who cannot get the disease because they either already had it andcannot get it again, or they simply cannot become infected because they took a vaccine. a.) Based upon the model given, what percentage of infected people become immune each day? Itmight be helpful to draw a "tank" diagram.b.) Find the eigenvalues and eigenvectors of this system. What classification can we give the origin,(0,0) in the S-1 phase plane? Feel free to round to two decimal places (e.g. 110.135 rounds to 110.14).c.) Suppose there are initially 600 thousand people who are initially susceptible and 50 thousandpeople who are initially infected. Solve the system of differential equations.d.) Based upon your solution, what is the largest number of people who are infectious in a single day?On what day is that?e.) How long will it be before fewer than 2 thousand people in the population are infected? This will beconsidered the end of the pandemic.

a) To find the percentage of infected people becoming immune each day, we need to determine the rate…

a.) Based upon the model given, what percentage of infected people become immune each day? It might be helpful to draw a "tank" diagram. b.) Find the eigenvalues and eigenvectors of this system. What classification can we give the origin, (0,0) in the S-1 phase plane? Feel free to round to two decimal places (e.g. 110.135 rounds to 110.14).

a.) Based upon the model given, what percentage of infected people become immune each day? It might be helpful to draw a "tank" diagram. b.) Find the eigenvalues and eigenvectors of this system. What classification can we give the origin, (0,0) in the S-1 phase plane? Feel free to round to two decimal places (e.g. 110.135 rounds to 110.14).

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

Suppose we are modeling the spread of a disease. People are categorized as either susceptible
or infectious (similar to our Module 7 discussion board). Those who are susceptible do not have the disease,
but could get it. Those who are infected currently have the disease. We assume this disease is not
transmittable by contact with an infectious person. Instead, we will assume it is something that is contracted
through environmental factors.
Define:
dt
= -.035.S
= .03S - .021
where
.
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
NOTE: Here we are dealing with the number of people, rather than the proportion of people, in each group.
This fact should not change your analysis in any significant way.
Anyone who is not susceptible or infected falls into a third category: immune. We do not concern ourselves
with this group, because they are people who cannot get the disease because they either already had it and
cannot get it again, or they simply cannot become infected because they took a vaccine.

a.) Based upon the model given, what percentage of infected people become immune each day? It
might be helpful to draw a "tank" diagram.
b.) Find the eigenvalues and eigenvectors of this system. What classification can we give the origin,
(0,0) in the S-1 phase plane? Feel free to round to two decimal places (e.g. 110.135 rounds to 110.14).
c.) Suppose there are initially 600 thousand people who are initially susceptible and 50 thousand
people who are initially infected. Solve the system of differential equations.
d.) Based upon your solution, what is the largest number of people who are infectious in a single day?
On what day is that?
e.) How long will it be before fewer than 2 thousand people in the population are infected? This will be
considered the end of the pandemic.

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