具有Beddington-DeAngelis功能反应和分布时滞的病毒动力学模型的稳定性  

The Stability of Virus Dynamics Model with Beddington-DeAngelis Functional Response and Distributed Time Delay

作　　者：周欣然 郑涛[1] 张龙[1] ZHOU Xinran;ZHENG Tao;ZHANG Long(College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China)

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830046

出　　处：《华南师范大学学报（自然科学版）》2020年第5期118-123,共6页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11861065,11361059,11771373,11702237);新疆维吾尔自治区自然科学基金项目(2019D01C076,2017D01C082);新疆维吾尔自治区教育厅重点实验室项目(2016D03022);新疆维吾尔自治区普通高等学校科研计划-创新团队项目(XJEDU2017T001);新疆大学博士创新项目(XJUBSCX-2017005)。

摘　　要：为了更真实地描述细胞被病毒感染的现象,在常见的病毒时滞模型基础上建立了一类具有Beddington-DeAngelis功能反应和分布时滞的病毒动力学模型.首先,讨论了该模型解的正性和有界性,得到了该模型的基本再生数R0;然后,证明了该模型的无病平衡点的局部渐近稳定性和全局渐近稳定性;最后,通过数值模拟验证了结论的有效性.A class of virus dynamics model with Beddington-DeAngelis functional response and distributed delay is established on the basis of the common virus time delay model to describe the phenomenon of virus infection in cells more accurately.Firstly,the positivity and boundedness of the solution of the model are discussed,and the basic reproduction number R0 of the model is obtained.Then,the local and global stability of the infection-free equilibrium of the model are proved.Further,numerical simulations are demonstrated to verify the theoretical results.

关 键 词：BEDDINGTON-DEANGELIS 分布时滞 基本再生数 LYAPUNOV函数 稳定性 

分 类 号：O175[理学—数学]