 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-207/3/f/solution

The removal rate is

\dot{R} = γ I

. Because

γ

is constant, its interior peak occurs when

I

is maximal. At such a point,

0 = \dot{I} = I (βS - γ),

and

I > 0

, so

S = \frac{γ}{β} .

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