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具有免疫应答和吸收效应的病毒感染模型分析

傅金波1,陈兰荪2   

  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

傅金波, 陈兰荪. 具有免疫应答和吸收效应的病毒感染模型分析[J]. 系统科学与数学, 2021, 41(1): 280-290.

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

研究了具有免疫应答和吸收效应的病毒动力 学模型的动力学行为. 通过构造适当的 Lyapunov 泛函, 使用 LaSalle 不变性原理,证明了基本再生数、$CTL$ 免疫再生数、抗体免疫再生数、$CTL$免疫竞争再生数和抗体免疫竞争再生数决定了模型的全局性态. 若基本再生数小于等于1, 病毒在体内清除. 若基本再生数大于1, 正解在满足条件$\max\{R_1,R_2\}\leq1<R_0<P_0$ 时趋于无免疫平衡点, 在满足条件$R_4\leq1<R_1<R_0<P_0$ 时趋于$CTL$主导平衡点, 在满足条件
$R_3\leq1<R_2<R_0<P_0$ 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).

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