Consider an SEIR model.  For adding $x \geq 0$ S->E event times we have:
\begin{equation}
S(t+1) &=& S(0) - (N_{se}(t) + x) \geq 0 \\
E(t+1) &=& E(0) + (N_{se}(t) + x) \geq 0
\end{equation}
such that $x$ is bounded by
$$
x \leq S(0) - N_{se}(t).
$$

Similarly for adding $x \geq 0$ E->I event times we have:
$$
x \leq E(0) + N_{se}(t) - N_{ei}(t).
$$

For deleting $x \geq 0$ S->E event times we have:
$$
x \leq E(0) + N_{se}(t) - N_{ei}(t)
$$
and for E->I event times we have;
$$
x \leq I(0) + N_{ei}(t) - N_{ir}(t).
$$