A virus infects by close contact, is most contagious during the winter and everyone who becomes infected stay infectious for an unlimited amount of time. In an isolated population with P people the infection rate by time t (in months after 1/1 2020) is proportional with the product of (1) The number of people infected (y(t)) (2) The number of people NOT infected (3) 1+ cos A tenth of the population is infected 1/1 2020. The task: Set up the differential equation that y(t) must satisfy and solve it. Call the proportionality constant k and explain each step in the solution.

A virus infects by close contact, is most contagious during the winter and everyone who becomes infected stay infectious for an unlimited amount of time. In an isolated population with P people the infection rate by time t (in months after 1/1 2020) is proportional with the product of (1) The number of people infected (y(t)) (2) The number of people NOT infected (3) 1+ cos A tenth of the population is infected 1/1 2020. The task: Set up the differential equation that y(t) must satisfy and solve it. Call the proportionality constant k and explain each step in the solution.

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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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 infects by close contact, is most contagious during the winter and everyone who
becomes infected stay infectious for an unlimited amount of time. In an isolated population with
P people the infection rate by time t (in months after 1/1 2020) is proportional with the product
of
(1) The number of people infected (y(t))
(2) The number of people NOT infected
(3) 1+ cos
A tenth of the population is infected 1/1 2020.
The task:
Set up the differential equation that y(t) must satisfy and solve it. Call the proportionality
constant k and explain each step in the solution.

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