The SEITL model extends the classical SEIR model by splitting the R compartement (recovered) to account for the dynamics and host heterogeneity of the immune response among the islanders. Following recovery, hosts remain temporarily protected against reinfection thanks to the cellular immune response (T-cells). Accordingly, they enter the T stage (temporary protection). Then, following down-regulation of the cellular response, the humoral immune response (antibodies) has a probability \(\alpha\) to reach a level sufficient to protect against reinfection. In this case, recovered hosts enter the L stage (long-term protection), but otherwise they remain unprotected and re-enter the susceptible pool (S).
The SEITL model can be described with five states (S, E, I, T and L) and five parameters:
and we define the effective contact rate \(\beta=R_0/D_\mathrm{inf}\), the rate of onset of infectiousness \(\epsilon=1/D_\mathrm{lat}\), the recovery rate \(\nu = 1/D_\mathrm{inf}\), the rate of loss of temporary immunity \(\tau=1/D_\mathrm{imm}\) and \(N = S + E + I + L + T\) the constant poulation size.
Based on the description of the outbreak and the information found in the literature we can make the following guess estimates:
You can now return to the practical session and write down the transition table of the SEITL model.