| 随机病原体-免疫模型的持久性与灭绝性 |
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| 引用本文： | 王晶囡,杨德中,刘胜男,王化娣,张志洋. 随机病原体-免疫模型的持久性与灭绝性[J]. 上海师范大学学报(自然科学版), 2020, 49(3): 311-322 |
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| 作者姓名： | 王晶囡 杨德中 刘胜男 王化娣 张志洋 |
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| 作者单位： | 哈尔滨理工大学 理学院, 黑龙江 哈尔滨 150080,哈尔滨理工大学 理学院, 黑龙江 哈尔滨 150080,哈尔滨理工大学 理学院, 黑龙江 哈尔滨 150080,哈尔滨理工大学 理学院, 黑龙江 哈尔滨 150080,哈尔滨理工大学 理学院, 黑龙江 哈尔滨 150080 |
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| 基金项目： | The National Natural Science Foundation of China (11801122); The Natural Science Foundation of Heilongjiang Province, China (A2018008) |
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| 摘 要： | 研究了带有环境白噪声的随机病原体-免疫模型，应用伊藤公式和Lyapunov函数，推导出随机模型全局唯一正解的存在性、病原体灭绝和均值强持久的充分条件.并利用数值模拟验证了理论结论.最后，讨论了在病原体与免疫细胞相互作用过程中，体内微环境噪声对病原体生存状态的影响.
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| 关 键 词： | 病原体-免疫 灭绝性 伊藤公式 持久性 |
| 收稿时间： | 2019-12-31 |
Persistence and extinction of the stochastic pathogen-immune model |
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| WANG Jingnan,YANG Dezhong,LIU Shengnan,WANG Huadi and ZHANG Zhiyang. Persistence and extinction of the stochastic pathogen-immune model[J]. Journal of Shanghai Normal University(Natural Sciences), 2020, 49(3): 311-322 |
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| Authors: | WANG Jingnan YANG Dezhong LIU Shengnan WANG Huadi ZHANG Zhiyang |
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| Affiliation: | School of Science, Harbin University of Science and Technology, Harbin 150080, Heilongjiang, China,School of Science, Harbin University of Science and Technology, Harbin 150080, Heilongjiang, China,School of Science, Harbin University of Science and Technology, Harbin 150080, Heilongjiang, China,School of Science, Harbin University of Science and Technology, Harbin 150080, Heilongjiang, China and School of Science, Harbin University of Science and Technology, Harbin 150080, Heilongjiang, China |
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| Abstract: | We study a stochastic pathogen-immune model with environmental white noise, and derive the existence of globally unique positive solution and the sufficient conditions for the extinction and the strong persistence in mean for pathogen by constructing Lyapunov function and Itô formula. In addition, we introduce numerical simulations to illustrate and verify the analytic results, and discuss the effect of microenvironmental noise on the survival status of pathogens during the interaction between pathogens and immune cells. |
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| Keywords: | pathogen-immune extinction Itô formula persistence |
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