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.

中文翻译：

---

关于随机环境中连续状态分支过程的灭绝

本文建立了一个在Lévy随机环境中具有时间不均匀竞争的连续状态分支过程的模型。提出了一些关于灭绝的结果，包括灭绝时间的分布，以大灭绝时间为条件的极限分布以及接近灭绝的渐近行为。本文还提供了一种新的时空变换，可用于类似模型的进一步探索。将结果应用于描述传染性种群动态的流行病模型和描述病毒载量动态的病毒模型。