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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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.

Question

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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