Table 1. Transition probabilities in prevalence theory for all models.

Event	Transition	Rate
SIS with social distancing
Infection	T(I + 1|I)	$\frac{\beta \left(t\right)(N-I)I}{N}$
Recovery	T(I − 1|I)	γI
SIS with vaccination
Infection	T(S − 1, I + 1|S, I)	$\frac{{\beta }_{0}SI}{N}$
Recovery	T(S + 1, I − 1|S, I)	γI
Incoming to S (non-vaccinated)	T(S + 1, I|S, I)	μN(1 − p(t))
Removal from I	T(S, I − 1|S, I)	μI
Removal from S	T(S − 1, I|S, I)	μS
SIS emergence
Infection	T(I + 1|I)	$\frac{\beta \left(t\right)(N-I)I}{N}+\nu (N-I)$
Recovery	T(I − 1|I)	γI