## Related questions with answers

A small, isolated mountain community with a population of 700 is visited by an outsider who carries influenza. After 6 weeks, 300 people are uninfected. a. Write an equation for the number of people who remain uninfected at time t (in weeks). b.Find the number still uninfected after 7 weeks. c. When will the maximum infection rate occur?

Solution

Verified(a) Spread of epidemic follows the general equation :

$y=\dfrac{N}{1+be^{-kt}}$

where, $y$ is the number of people infected at time $t$.

From $P10$ in section $10.4$, the number of uninfected people (if one is infected initially) is given by $y'(t)=\dfrac{N(N-1)}{N-1+e^{kt}}$

For our problem, $N=700$

$\begin{align*} y'(6)&=\dfrac{700\times 699}{699+e^{6k}}\\ (699+e^{6k})300&=700\times 699\\ e^{6k}&=932\\ \color{#c34632}k&\color{#c34632}=1.140 \end{align*}$

Number of unaffected people, $\color{#c34632}y'(t)=\dfrac{489300}{699+e^{1.140t}}$

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