Mathematics

CLC number: O211.6

Several Properties of Branching Processes with Migration and Affected by Viral Infectivity in Random Environments

随机环境中具有迁移且受病毒传染性影响的分枝过程的若干性质

School of Mathematics and Statistics, Suzhou College, Suzhou 234000, Anhui, China (宿州学院　数学与统计学院，安徽　宿州　234000)

^† Corresponding author. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 3 February 2025

Abstract

In this paper, a model of branching processes with migration and affected by viral infectivity in independent and identically distributed (i.i.d.) random environments is established firstly. Then the Markov property, conditional probability generating function and conditional expectation of the model are studied. Finally, under certain conditions, some sufficient conditions for certain extinction of processes are given, and some related theories of branching processes in random environments are generalized.

摘要

本文首先建立了独立同分布随机环境中具有迁移且受病毒传染性影响的分枝过程的模型。然后，研究了该模型的马氏性、条件概率母函数和条件期望的性质。最后，在一定条件下给出过程必然灭绝的一些充分条件，从而推广了随机环境中分枝过程的相关理论。