The <SI model> has two compartments and one transition,
$$
S\xrightarrow{\,\beta SI/N\,}I,
$$
where $S$ and $I$ are the numbers susceptible and infectious and $\beta>0$ is the per-infective transmission-rate parameter under frequency-dependent homogeneous mixing.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 207 / 3 / a / Solution

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{wiki=Compartmental_models_in_epidemiology#The_SI_model}

The SI model divides a closed population into susceptible and permanently infectious compartments. Under frequency-dependent homogeneous mixing,
$$
\dot S=-\beta SI/N,
\qquad
\dot I=\beta SI/N,
$$
and <conservation of population> gives $S+I=N$.

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