Pending infections at quarantine in a delayed epidemic model ($E(T)=\tau rI(T)S(T)+O({\tau }^2)$)

When exposed animals remain in a not-yet-infective compartment for a fixed incubation period $\tau$, stopping all new exposure does not cancel the pending case transfers. At isolation time $T$, their number is $E(T)={\int }_{T-\tau }^{T}rI(s)S(s)ds=\tau rI(T)S(T)+O({\tau }^2)$ for smooth profiles. Eventual cases therefore include this pipeline in addition to case transfers already completed by $T$. The interpretation depends on the compartment definition: a strictly unexposed susceptible compartment would instead lose these animals at exposure.