I understand that for a birth process with rate $\exp(\lambda_n)$, explosion occurs if there are infinitely many individuals born in finite time, which is iff $\sum \frac{1}{\lambda_n}<\infty$.
My question is how do I understand explosion for a birth and death process with rate $\exp(\lambda_n)$ and $\exp(\mu_n)$ respectively. In particular, what does it mean to say "find a birth process that strictly dominated the birth and death process"?