On the extinction of continuous-state branching processes in random environments

Xiangqi Zheng; Xiangqi Zheng

doi:10.3934/math.2021011

AIMS Mathematics

2021, Volume 6, Issue 1: 156-167. doi: 10.3934/math.2021011

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Research article

On the extinction of continuous-state branching processes in random environments

Xiangqi Zheng ^,

Department of Mathematics, East China University of Science and Technology, People's Republic of China

Received: 27 April 2020 Accepted: 16 July 2020 Published: 09 October 2020
MSC : 35A01, 60H05

This paper establishes a model of continuous-state branching processes with time inhomogeneous competition in Lévy random environments. Some results on extinction are presented, including the distribution of the extinction time, the limiting distribution conditioned on large extinction times and the asymptotic behavior near extinction. This paper also provides a new time-space transformation which can be used for further exploration in similar models. The results are applied to an epidemic model to describe the dynamics of infectious population and a virus model to describe the dynamics of viral load.
- branching processes,
- asymptotic behavior,
- extinction,
- time-space transformation,
- epidemic,
- virus
Citation: Xiangqi Zheng. On the extinction of continuous-state branching processes in random environments[J]. AIMS Mathematics, 2021, 6(1): 156-167. doi: 10.3934/math.2021011

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Abstract

This paper establishes a model of continuous-state branching processes with time inhomogeneous competition in Lévy random environments. Some results on extinction are presented, including the distribution of the extinction time, the limiting distribution conditioned on large extinction times and the asymptotic behavior near extinction. This paper also provides a new time-space transformation which can be used for further exploration in similar models. The results are applied to an epidemic model to describe the dynamics of infectious population and a virus model to describe the dynamics of viral load.

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