 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2006/ii/paper-3/6b/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

Since

S \leq N

, the infected population satisfies

\dot{I} = (r S - a) I \leq (r N - a) I

. Integration gives

I (t) \leq I (0) e^{(r N - a) t}

. Hence

r N < a

forces the infected population to decrease exponentially from the outset: there is no epidemic outbreak.

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