 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-1/6c/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Substitute

S = N - I

and

S = N - I

\dot{I} = β (N - I) I - ν I, \dot{I} = β (N - I) I - ν I .

Besides the origin, solve both nullcline equations. Eliminating one infected population gives

I_{*} = \frac{N N - ν ν / ( β β )}{ν / β + N}, I_{*} = \frac{N N - ν ν / ( β β )}{ν / β + N} .

The assumed epidemic threshold inequality makes both positive.

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