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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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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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.
AbstractList 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.
Author Zheng, Xiangqi
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10.1007/978-3-642-81046-6_44
10.1016/j.spa.2018.09.011
10.1017/S0021900200005039
10.1002/mma.6493
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10.1128/JVI.00127-10
10.1214/EJP.v18-2774
10.1007/978-981-15-1576-7_1
10.1007/978-3-642-35858-6
10.1214/14-AIHP621
10.1007/s10473-019-0104-y
10.1016/j.spa.2013.08.009
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Snippet This paper establishes a model of continuous-state branching processes with time inhomogeneous competition in Lévy random environments. Some results on...
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SubjectTerms asymptotic behavior
branching processes
epidemic
extinction
time-space transformation
virus
Title On the extinction of continuous-state branching processes in random environments
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