SEIR project
The SEIR model introduces an exposed class for infected individuals who are not yet infectious:
\[\frac{dS}{dt}=-\beta\frac{SI}{N},\quad \frac{dE}{dt}=\beta\frac{SI}{N}-\sigma E,\quad \frac{dI}{dt}=\sigma E-\gamma I,\quad \frac{dR}{dt}=\gamma I.\]The mean exposed duration is \(1/\sigma\), while the mean infectious duration is \(1/\gamma\).
Investigation
Compare an SEIR trajectory with an SIR model using similar transmission and recovery assumptions. Vary \(\sigma\) to examine how the latent period changes the timing of infectious prevalence.
Capacity extension
Map a defined fraction or delayed flow of severe cases into a hospital compartment and compare predicted occupancy with a capacity threshold.
Project outcome. Show how adding a biologically meaningful latent stage changes epidemic timing and downstream demand.