SEIR model

The SEIR model divides a population into susceptible, exposed, infectious, and recovered compartments.

The force of infection is the instantaneous infection hazard experienced by a susceptible individual. Under homogeneous frequency-dependent mixing it is $\beta I(t)/N$.

For a closed homogeneous epidemic, integrating $dS/dR$ relates the ultimately susceptible population to cumulative infections through an exponential equation.

The relation constrains the final outcome of compartmental models rather than describing their whole time-dependent solution.