A flu virus is spreading in a community which has a fixed population of $N$ people. Scientists dis

Question

A flu virus is spreading in a community which has a fixed population of $N$ people. Scientists discover that at time $t$ weeks from the beginning, the rate of change of the number of people who are infected is proportional to the product of the number of people infected, $I$, and the number of people who are not infected.

Write down a differential equation relating $I$ and $t$.[1]

It is noted that at the beginning, $1\%$ of the people in the community is infected with the virus. $12$ weeks later, the proportion of people infected in the community has risen to $25\%$.

By solving the differential equation obtained in part (i), show that $I=\frac{N}{99\left( {{33}^{-\frac{t}{12}}} \right)+1}$.[6]

Accepted Answer

(i) $\dfrac{\mathrm dI}{\mathrm dt}=kI(N-I)$, $k>0$ (ii) $I=\dfrac{N}{99\left(33^{-t/12}\right)+1}$

2021 HCI P1 Q10

2021 HCI P1 Q10

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