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.