Epidemic Problem- spread of

• November 6th 2012, 12:59 AM
NettieL
Epidemic Problem- spread of
Can someone tell me how I ought the answer this question:
'Suppose that an epidemic in a community of 50,000 starts with 80 people infected, and that 15 days later, 640 are infected. How many are infected 25 days into the epidemic?'

The correct answer is supposd to be 2483, and the question should be based on the logistic growth model.
Please help, as I have no idea what to do!!
• November 6th 2012, 05:36 AM
tom@ballooncalculus
Re: Epidemic Problem- spread of
Using

\displaystyle \begin{align*} P\ &= \ \frac{K P_0\ e^{rt}}{K + P_0\ (e^{rt} - 1)} \\ \\ &= \ \frac{K P_0}{(K - P_0)\ e^{-rt} + P_0} \end{align*}

from Logistic function - Wikipedia, the free encyclopedia,

... you can plug in K = 50,000, P0 = 50, t = 15 and P = 640 to find r, then use that to find P when t = 25.