| Event | Transition | Jump intensity |
|---|---|---|
| Infection | \((s,e,i,t,l) \to (s-1,e+1,i,t,l)\) | \(\beta si/N\) |
| Onset of infectiousness | \((s,e,i,t,l) \to (s,e-1,i+1,t,l)\) | \(\epsilon e\) |
| Recovery and onset of temporary immunity | \((s,e,i,t,l) \to (s,e,i-1,t+1,l)\) | \(\nu i\) |
| Onset of long-term immunity | \((s,e,i,t,l) \to (s,e,i,t-1,l+1)\) | \(\alpha \tau t\) |
| Defficient long-term immunity | \((s,e,i,t,l) \to (s+1,e,i,t-1,l)\) | \((1-\alpha) \tau t\) |
Now you can come back to the practical.