The linear <SEIR model> with a constant susceptible-to-exposed intensity is
$$
\dot S=-q_{SE}S,
\qquad
\dot E=q_{SE}S-q_{EI}E,
\qquad
\dot I=q_{EI}E-q_{IR}I,
\qquad
\dot R=q_{IR}I.
$$
Adding the four equations confirms <conservation of population>: $S+E+I+R=N$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 207 / 2 / d / i / Solution

If every transition transfers individuals between compartments without births, deaths, immigration, or emigration, the sum of all compartment sizes is constant.


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