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

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...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 1; pp. 156 - 167
Main Author Zheng, Xiangqi
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
asymptotic behavior
branching processes
epidemic
extinction
time-space transformation
virus
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021011