SEIR model
The SEIR model introduces an exposed compartment for individuals who have been infected but are not yet infectious.
\[S\longrightarrow E\longrightarrow I\longrightarrow R.\]Equations
\[\frac{dS}{dt}=-\beta\frac{SI}{N},\]\[\frac{dE}{dt}=\beta\frac{SI}{N}-\sigma E,\]\[\frac{dI}{dt}=\sigma E-\gamma I,\]\[\frac{dR}{dt}=\gamma I.\]The mean duration of the exposed stage is \(1/\sigma\) when progression occurs at a constant per-capita rate \(\sigma\).
Why exposure matters
The exposed compartment introduces a delay between infection and infectiousness and can substantially alter epidemic timing.
Key idea. SEIR models distinguish becoming infected from becoming infectious.