一类带有饱和发生率和Logistic增长的随机病毒感染模型的灭绝性及平稳分布
Extinction and Stationary Distribution of a Classic Stochastic Viral Infection Model with Saturation Rate and Logistic Growth
DOI: 10.12677/AAM.2018.75072, PDF,   
作者: 罗 超, 张晓丹：北京科技大学数理学院，北京
关键词: 饱和发生率；Logistic增长；平稳分布；Saturation Rate； Logistic Growth； Stationary Distribution
摘要: 本文研究了具有饱和发生率和logistic增长的随机病毒感染模型，当病毒感染细胞基本再生数R0<1时，确定未感染细胞的有界性和病毒感染细胞的灭绝性；当病毒感染细胞基本在生数R0>1时，构建适当的Lyapunov函数，确定平稳分布的充分条件。它显示了病毒感染在机体内持久性存在。
Abstract: In this paper, a classic stochastic viral infection model with saturation rate and logistic growth is researched. To be start, when R0<1, the boundeness of uninfected cells and the extinction of in-fected cells are discussed. Then, when R0>1 , some available Lyapunov functions are constricted and some sufficient conditions are established for stationary distribution. The theory verifies that infected cells keep persistence in vivo.
文章引用：罗超, 张晓丹. 一类带有饱和发生率和Logistic增长的随机病毒感染模型的灭绝性及平稳分布[J]. 应用数学进展, 2018, 7(5): 609-616. https://doi.org/10.12677/AAM.2018.75072

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