On linear birth-and-death processes in a random environment

被引：24

作者：

Bacaer, Nicolas ^{[1
,2
]}

Ed-Darraz, Abdelkarim ^{[1
,2
,3
]}

机构：

[1] IRD, Bondy, France

[2] Univ Paris 06, UMMISCO, UMI209, Bondy, France

[3] Cadi Ayyad Univ, Dept Math, Marrakech, Morocco

来源：

JOURNAL OF MATHEMATICAL BIOLOGY | 2014年 / 69卷 / 01期

关键词：

Random environment; Birth-and-death process; Extinction probability; Basic reproduction number; BRANCHING-PROCESSES; LYAPUNOV EXPONENTS; EPIDEMIC; POPULATION;

D O I：

10.1007/s00285-013-0696-0

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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 is , the key point being to identify a suitable definition of for such a result to hold.

引用

收藏

页码：73 / 90

页数：18

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