Quarantine

Quarantine restricts contacts of exposed individuals whose infection status is uncertain, with monitoring to detect illness. It differs from isolation of recognized infected or ill individuals. An incubation period quantile can enter a duration calculation, but assumptions about exposure time, symptom detection and infectiousness are needed before the calculation describes transmission risk.

Before isolation, the closed SIR model has first integral $I+S-(a/r)\log S$. If quarantine occurs at the first crossing $I=I_{\ast }$, the corresponding susceptible count $S_{\ast }$ is the root on the outbreak branch of $I_{\ast }+S_{\ast }-(a/r)\log S_{\ast }=I_0+S_0-(a/r)\log S_0$. Immediate prevention of further transmission makes the number infected among the initial susceptible class equal to $S_0-S_{\ast }$.

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.