On linear birth-and-death processes in a random environment
We study the probability of extinction for single-type and multi-type continuous-time linear birth-and-death processes in a finite Markovian environment. The probability of extinction is equal to 1 almost surely if and only if the basic reproduction number $$R_0$$R0 is $$\le 1$$≤1, the key point being to identify a suitable definition of $$R_0$$R0 for such a result to hold.