Consider a beehive of 100,000 bees. Suppose that an outbreak of a virus occurs in the beehive. Once a bee becomes infected, the bee remains infected and does not recover. The virus does not kill the bees. Let I(t) be the number (in thousands) of bees that are infected at time t days after the start of the outbreak. The rate of increase of I at time t is proportional to the product of the number of bees which are infected at time t, and the number of bees which are not infected at time t. (a) I(t) satisfies the ODE dI dt. = BI(100-I)
Consider a beehive of 100,000 bees. Suppose that an outbreak of a virus occurs in the beehive. Once a bee becomes infected, the bee remains infected and does not recover. The virus does not kill the bees. Let I(t) be the number (in thousands) of bees that are infected at time t days after the start of the outbreak. The rate of increase of I at time t is proportional to the product of the number of bees which are infected at time t, and the number of bees which are not infected at time t. (a) I(t) satisfies the ODE dI dt. = BI(100-I)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
(b) Find the general solution of the ODE.
(c) The outbreak begins with 100 infected bees at time t = 0. 3 days later there are 1000
infected bees. Find I(t) in terms of t.
Transcribed Image Text:Consider a beehive of 100,000 bees. Suppose that an outbreak of a virus occurs in the beehive.
Once a bee becomes infected, the bee remains infected and does not recover. The virus does
not kill the bees.
Let I(t) be the number (in thousands) of bees that are infected at time t days after the start of
the outbreak. The rate of increase of I at time t is proportional to the product of the number
of bees which are infected at time t, and the number of bees which are not infected at time t.
(a) I(t) satisfies the ODE
dI
dt
BI(100 - I)
where 3 > 0 is a constant. Explain why, with reference to the information given above.
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