A virus spreads by contact and if you get infected you stay contagious. In an isolated population with P persons (no-one dies or are born) the rate of infection at time t (in months after 1/1 2020) is proportional to the product of 1. the number y(t) that are infected, 2. the number that are not infected 3. eat where a is a negative number depending on disease preventive measures. One tenth of the population is infected 1/1-2020. (a) Write out the differential equation y(t) must satisfy and solve it (call the proportionality constant k and remember to explain each step of your solution carefully. Are there for instance any constant solutions?).
A virus spreads by contact and if you get infected you stay contagious. In an isolated population with P persons (no-one dies or are born) the rate of infection at time t (in months after 1/1 2020) is proportional to the product of 1. the number y(t) that are infected, 2. the number that are not infected 3. eat where a is a negative number depending on disease preventive measures. One tenth of the population is infected 1/1-2020. (a) Write out the differential equation y(t) must satisfy and solve it (call the proportionality constant k and remember to explain each step of your solution carefully. Are there for instance any constant solutions?).
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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![A virus spreads by contact and if you get infected you stay contagious. In an isolated population with P persons
(no-one dies or are born) the rate of infection at time t (in months after 1/1 2020) is proportional to the product of
1. the number y(t) that are infected,
2. the number that are not infected
3. eat where a is a negative number depending on disease preventive measures.
One tenth of the population is infected 1/1-2020.
(a) Write out the differential equation y(t) must satisfy and solve it (call the proportionality constant k and
remember to explain each step of your solution carefully. Are there for instance any constant solutions?).
(b) Find a relation between L = lim->00 y(t), a, Pand k. What can you say about L when a is very small?
What can you say about L when a is very big?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78f3f25b-2eb2-4186-b342-f9f487e8326d%2Fea9384e7-3460-4c58-8160-635d94d19278%2F8e335o_processed.png&w=3840&q=75)
Transcribed Image Text:A virus spreads by contact and if you get infected you stay contagious. In an isolated population with P persons
(no-one dies or are born) the rate of infection at time t (in months after 1/1 2020) is proportional to the product of
1. the number y(t) that are infected,
2. the number that are not infected
3. eat where a is a negative number depending on disease preventive measures.
One tenth of the population is infected 1/1-2020.
(a) Write out the differential equation y(t) must satisfy and solve it (call the proportionality constant k and
remember to explain each step of your solution carefully. Are there for instance any constant solutions?).
(b) Find a relation between L = lim->00 y(t), a, Pand k. What can you say about L when a is very small?
What can you say about L when a is very big?
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