An epidemic spreads through a community so that t weeks after its outbreak, the
ID: 2861033 • Letter: A
Question
An epidemic spreads through a community so that t weeks after its outbreak, the number of people who have been infected is given by the form f(t) = (B) / (1 + Ce-kt) Where B is the number of residents in the community who are susceptible to the disease. If 1/5 of the susceptible residents were infected initially and 1/2 had been infected by the end of the fourth week, what fraction of the susceptible residents will have been infected by the end of the fourth week? What fraction of the susceptible residents will have bee infected by the end of the eighth week?
Explanation / Answer
at t=0, f(t)=f(0)=B/5
f(4)=B/2
from these two we will find value of constant C,k.
B/5= B/(1 + Ce-k*0) ; 5=1+C; C=4
B/2= B/(1 + Ce-k*4) ;1= Ce-k*4=4e-k*4; k=ln4/4
now we have to find f(8)
=B/(1 + Ce-k*8)=B/(1 + 4e-2ln4)=4B/5
so 4/5th susceptible residents will have bee infected by the end of the eighth week.