title: On linear birth-and-death processes in a random environment.
abstract: 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) is ≤ 1, the key point being to identify a suitable definition of R(0) for such a result to hold.
authors.affiliation: IRD and University Paris 6, UMI209-UMMISCO, Bondy, France, nicolas.bacaer@ird.fr.
authors.forename: Nicolas
authors.initials: N
authors.lastname: Bacaër
authors.forename: Abdelkarim
authors.initials: A
authors.lastname: Ed-Darraz
mesh_terms: D050936:Basic Reproduction Number; D003198:Computer Simulation; D017753:Ecosystem; D053476:Extinction, Biological; D008390:Markov Chains; D008954:Models, Biological; D011157:Population Dynamics