The SEITL model can be described with five states (S, E, I, T and L) and five parameters:

1. basic reproductive number (\(R_0\))
2. latent period (\(D_\mathrm{lat}\))
3. infectious period (\(D_\mathrm{inf}\))
4. temporary-immune period (\(D_\mathrm{imm}\))
5. probability of developing a long-term protection (\(\alpha\)).

and the following deterministic equations:

\[ \begin{cases} \begin{aligned} \frac{dS}{dt} &= - \beta S \frac{I}{N} + (1-\alpha) \tau T\\ \frac{dE}{dt} &= \beta S \frac{I}{N} - \epsilon E\\ \frac{dI}{dt} &= \epsilon E - \nu I\\ \frac{dT}{dt} &= \nu I - \tau T\\ \frac{dL}{dt} &= \alpha \tau T\\ \end{aligned} \end{cases} \]

where \(\beta=R_0/D_\mathrm{inf}\), \(\epsilon=1/D_\mathrm{lat}\), \(\nu = 1/D_\mathrm{inf}\), \(\tau=1/D_\mathrm{imm}\) and \(N = S + E + I + L + T\) is constant.

As you saw in the lecture, there is an analogy between the deterministic equations and the algorithm that performs stochastic simulations of the model. In that sense, the deterministic equations are a description of the stochastic model, too.

You can now return to the practical session and design the flowchart of the SEITL model. If you need more help, you can check our solution (note that this is one among several possible solutions).