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In: Advanced Math

The total number of people infected with a virus often grows like a logistic curve. Suppose...

The total number of people infected with a virus often grows like a logistic curve. Suppose that 20 people originally have the virus, and that in the early stages of the virus (with time, t, measured in weeks), the number of people infected is increasing exponentially with r=1.8. It is estimated that, in the long run, approximately 6250 people become infected.

(a) Use this information to write down a logistic differential equation for population P

dP/dt=

Then find the solution:

P=

(b) Sketch a graph of your solution. Use your graph to estimate the length of time until the rate at which people are becoming infected starts to decrease. What is the vertical coordinate at this point? vertical coordinate =

(In practice, it may be easier to plot your answer for dP/dt instead, and pick the value of P for which it is maximal.)

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Expert Solution

Colby Messinger answered 5 months ago
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