[1]田小江,谭远顺,颜 莉.一类具有年龄结构的溶瘤病毒模型的动力学行为分析[J].南京师大学报(自然科学版),2024,(03):8-14.[doi:10.3969/j.issn.1001-4616.2024.03.002]
　Tian Xiaojiang,Tan Yuanshun,Yan Li.Global Dynamic Analysis of an Oncolytic Virus Model with Age Structure[J].Journal of Nanjing Normal University(Natural Science Edition),2024,(03):8-14.[doi:10.3969/j.issn.1001-4616.2024.03.002]
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一类具有年龄结构的溶瘤病毒模型的动力学行为分析()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
期数:
2024年03期
页码:
8-14
栏目:
数学
出版日期:
2024-09-15

文章信息/Info

Title:
Global Dynamic Analysis of an Oncolytic Virus Model with Age Structure
文章编号:
1001-4616(2024)03-0008-07
作者:
田小江; 谭远顺; 颜 莉
(重庆交通大学数学与统计学院,重庆 400074)
Author(s):
Tian Xiaojiang; Tan Yuanshun; Yan Li
(School of Mathematics and Statistics,Chongqing Jiaotong University,Chongqing 400074,China)
关键词:
年龄结构病毒模型; 溶瘤病毒; 稳态; Lyapunov函数; 全局稳定性
Keywords:
age-structured virus model; oncolytic virus; steady state; Lyapunov functional; global stability
分类号:
O175.1
DOI:
10.3969/j.issn.1001-4616.2024.03.002
文献标志码:
A
摘要:
本文考虑到溶瘤病毒感染肿瘤细胞的可能性取决于可以感染的肿瘤细胞的数量,引入了频率依赖性函数,建立了一类具有年龄结构的溶瘤病毒感染模型,并研究了模型的全局动力学行为.首先证明了模型解的存在唯一性,计算了基本再生数R0,得到了稳态的存在定理.之后通过分析特征方程特征根的分布,得到了稳态的局部稳定性结论.最后通过构造Lyapunov函数和运用LaSalle不变集原理,得到模型无感染稳态E0和感染稳态E*的全局稳定性结论:当R0<1时,无感染稳态E0是全局渐近稳定的; 当R0>1时,感染稳态E*是全局渐近稳定的.
Abstract:
In this paper,considering that the possibility of oncolytic virus infection of tumor cells depends on the number of tumor cells that can be infected,a frequency-dependent function is introduced to establish an age-structured oncolytic virus infection model,and the global dynamic behavior of the model is studied. Firstly,the existence and uniqueness of the solution of the model are proved,the basic reproduction number R0 is calculated,and the existence theorem of the steady state is obtained. Then,by analyzing the distribution of the characteristic roots of the characteristic equation,the local stability conclusion of the steady state is obtained. Finally,by constructing the Lyapunov function and using the LaSalle invariant set principle. The global stability theory of the infection-free steady state E0 and the infected steady state E* are obtained:When R0<1,the infection-free steady state E0 is globally asymptotically stable; when R0>1,the infected steady state E* is globally asymptotically stable.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2023-10-18.
基金项目:国家自然科学基金项目(12271068、11961024).
通讯作者:谭远顺,博士,教授,博士生导师,研究方向:生物数学模型的建立与分析. E-mail:tanys625@163.com
更新日期/Last Update: 2024-09-15