 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-3/13e/b/solution

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

With

S_{i} ≃ N_{i}

, the infective equations become

\dot{I}_{i} = β \sum_{j} \frac{N _{i} C _{ij}}{N _{j}} I_{j} - γ I_{i} = β \sum_{j} C_{ji} I_{j} - γ I_{i},

where reciprocity was used. For a column vector

I

\dot{I} = γ (L - 1) I, L = \frac{β}{γ} C^{T} .

Therefore

I (t) = e^{γ (L - 1) t} I (0) .

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