= Small-delay expansion of an epidemic transfer rate
{title2=$rI(t-\tau)S(t-\tau)=rIS+\tau rIS\{a+r(I-S)\}+O(\tau^2)$}
For a smooth delayed-transfer epidemic model, the incidence $rI(t-\tau)S(t-\tau)$ equals $rIS-r\tau(\dot I S+I\dot S)+O(\tau^2)$. Substituting the zero-delay equations only inside the correction gives $rIS+\tau rIS\{a+r(I-S)\}+O(\tau^2)$. The correction has opposite signs in the receiving and departing <compartmental model>[compartments], preserving their transfer balance.
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