• 论文 •

### 具有免疫应答和吸收效应的病毒感染模型分析

1. 1. 闽南科技学院, 泉州 362332;2. 中国科学院数学与系统科学研究院数学研究所, 北京 100190
• 出版日期:2021-01-25 发布日期:2021-03-11

FU Jinbo, CHEN Lansun. Analysis for Viral Infection Model with Absorption and Immune Response[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(1): 280-290.

### Analysis for Viral Infection Model with Absorption and Immune Response

FU Jinbo1 ,CHEN Lansun2

1. 1. Minnan Science and Technology Institute, Quanzhou 362332; 2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190
• Online:2021-01-25 Published:2021-03-11

$R_3\leq1<R_2<R_0<P_0$ 时趋于抗体主导平衡点, 在满足条件$1<R_3<R_0<P_3,~1<R_4<R_0<P_3$ 时趋于正平衡点,据此获得了无病平衡点、无免疫平衡点、$CTL$主导平衡点、抗体主导平衡点和正平衡点全局渐近稳定的充分条件,推广了Dominik  (2003) 的工作.

In this paper, the dynamical behaviors of the virus dynamics model with immune response and absorption are studied. By constructing suitable Lyapunov functionals, using the LaSalle invariance principle, have shown that basic reproductive number, $CTL$ immune response reproductive number and antibody immune response reproductive number, $CTL$ immune response competition reproductive number, antibody immune response competition reproductive number determine the global properties of the model. If the basic reproduction number is less than or equal to 1, the virus is cleared. For the basic reproduction number is greater than 1, positive solutions approach to an immune-free equilibrium if conditions are met $\max\{R_1,R_2\}\leq1<R_0<P_0$, to a $CTL$dominant equilibrium if conditions are met $R_4\leq1<R_1<R_0<P_0$,to a antibody dominant equilibrium if conditions are met $R_3\leq1<R_2<R_0<P_0$ , and to an endemic equilibrium conditions are met $1<R_3<R_0<P_3,~1<R_4<R_0<P_3$, obtained the sufficient conditions of the global stability of the infection-free equilibrium, the immune-free equilibrium, the $CTL$ dominant equilibrium, the antibody dominant equilibrium and the positive equilibrium, generalized the work of  Dominik  (2003).

()
 [1] 孙传成，邱志鹏，杨晓敏. 一类具有媒体影响的媒介传染病模型的分析[J]. 系统科学与数学, 2017, 37(9): 2028-2038. [2] 陈辉，徐瑞. 一类含潜伏期和CTL免疫反应的病毒感染模型的全局渐近稳定性[J]. 系统科学与数学, 2017, 37(2): 632-640. [3] 熊友兵;李红智. 具有时滞及B-D功能反应的食物链系统周期解的存在性与全局渐近稳定性[J]. 系统科学与数学, 2008, 28(3): 288-301.