= Quarantine threshold in the SIR model
{title2=$I_*+S_*-\frac ar\log S_*=I_0+S_0-\frac ar\log S_0$}
Before isolation, the closed <SIR model> has <first integral of an ordinary differential equation>[first integral] $I+S-(a/r)\log S$. If <quarantine> occurs at the first crossing $I=I_*$, the corresponding <susceptible individual>[susceptible] count $S_*$ is the <root of a polynomial>[root] on the outbreak branch of $I_*+S_*-(a/r)\log S_*=I_0+S_0-(a/r)\log S_0$. Immediate prevention of further transmission makes the number <infectious disease>[infected] among the initial <susceptible individual>[susceptible] class equal to $S_0-S_*$.
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