A curve representing the total number of people, P, infected with a virus often has the shape of a logistic curve of the form

with time t in weeks. Suppose that 10 people originally have the virus and that in the early stages the number of people infected is increasing approximately exponentially, with a continuous growth rate of 1.78. It is estimated that, in the long run, approximately 5000 people will become infected.
(a) What should we use for the parameters k and L?
(b) Use the fact that when t = 0, we have P = 10, to find C.
(c) Now that you have estimated L, k, and C, what is the logistic function you are using to model the data? Graph this function.
(d) Estimate the length of time until the rate at which people are becoming infected starts to decrease. What is the value of P at this point?

Transcribed Image Text:

P = L 1+ Ce-kt'