具有混合切换的随机丙型肝炎病毒感染模型的长期性行为
Long Time Behavior of Stochastic Hepatitis C Virus Infection Model with Mixed Switching
DOI: 10.12677/PM.2020.105053, PDF,    国家自然科学基金支持
作者: 黄露秋, 吕 超, 潘玉婷, 黄在堂：南宁师范大学数学与统计学院，广西 南宁
关键词: 随机HCV模型；灭绝性；持久性；不变概率测度；马尔科夫链；Stochastic HCV Model； Extinction； Permanence； Invariant Probability Measure； Markov Chain
摘要: 本文主要研究具有混合切换的随机丙型肝炎病毒感染模型(HCV模型)的灭绝性和持久性。首先，证明了随机HCV模型解的存在性唯一性。其次，利用费勒性质、不变控制集和Krylov-Bogoliubov定理等理论，证明了随机HCV模型的不变概率测度的存在唯一性。最后，运用强遍历性定理、波莱尔康特立引理和迭代对数定律等理论，获得了随机HCV模型的灭绝性和持久性的条件。
Abstract: This paper mainly studies the extinction and persistence of a stochastic hepatitis C virus infection model (HCV model) with mixed switching. First, we prove the existence and uniqueness of the so-lution of the stochastic HCV model. Secondly, we prove the existence and uniqueness of the invariant probability measure of the stochastic HCV model by using the theory of Feller property, invariant control set and Krylov Bogoliubov theorem. Finally, by using the strong ergodicity theorem, Borel-Cantelli lemma and iterated logarithm law, the conditions of extinction and persistence of the stochastic HCV model are obtained.
文章引用：黄露秋, 吕超, 潘玉婷, 黄在堂. 具有混合切换的随机丙型肝炎病毒感染模型的长期性行为[J]. 理论数学, 2020, 10(5): 433-447. https://doi.org/10.12677/PM.2020.105053

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