= Solution
In the <SIR model>, $S,I,R$ count susceptible, infectious, and recovered immune individuals. The closed population has $S+I+R=N+1$. Under homogeneous mixing, use the paper's <mass-action infection> convention: each susceptible has infection <hazard function> $\beta I$, so the population infection rate is $\beta SI$. Each infectious individual recovers with <hazard function> $\gamma$, giving population recovery rate $\gamma I$ and mean infectious duration $1/\gamma$.
\Image[/past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2016/iii/paper-207-sir-states.png]
{title=SIR compartment transitions with infection flow beta S I and recovery flow gamma I}
The arrows are one-way: recovered individuals are immune, and there are no demographic entries or exits. The <transition intensities> attached to the arrows are population flow rates, rather than individual <hazard functions>.
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