Stability of delayed virus infection model with a general incidence rate and adaptive immune response

被引:0
作者
Chen, Zhimin [1 ]
Liu, Xiuxiang [1 ]
Xie, Zhongzhong [1 ]
机构
[1] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China
来源
APPLICATIONS AND APPLIED MATHEMATICS-AN INTERNATIONAL JOURNAL | 2018年 / 13卷 / 02期
关键词
General incidence rate; Cellular immunity response; Humoral immunity response; Disstributed delay; Basic reproductive numbers; Global stability; Lyapunov functional;
D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We present the dynamical behaviors of a virus infection model with general infection rate, immune responses and two intracellular delays which describe the interactions of the HIV virus, target cells, CTL cells and antibodies within host. Three factors are incorporated in this model: (1) the intrinsic growth rate of uninfected cells, (2) a nonlinear incidence rate function considering both virus-tocell infection and cell-to-cell transmission, and (3) a nonlinear productivity and removal function. By the method of Lyapunov functionals and LaSalle's invariance principle, we show that the global dynamics of the model is determined by the reproductive numbers for viral infection R-0, for antibody immune response R-1, for CTL immune response R-2, for CTL immune competition R-3 and for antibody immune competition R-4. The numerical simulations are given to illustrate our theoretical results.
引用
收藏
页码:677 / 708
页数:32
相关论文
共 34 条
[1]  
DIEKMANN O, 1990, J MATH BIOL, V28, P365
[2]  
Dubey B, 2015, APPL APPL MATH, V10, P718
[3]   STABILITY OF HUMORAL IMMUNITY VIRUS INFECTION MODEL WITH GENERAL INCIDENCE RATE AND DISTRIBUTED DELAYS [J].
Elaiw, A. M. ;
Alhejelan, A. ;
Shehata, A. M. .
MISKOLC MATHEMATICAL NOTES, 2016, 17 (01) :209-230
[4]   Stability analysis of general viral infection models with humoral immunity [J].
Elaiw, A. M. ;
AlShamrani, N. H. .
JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2016, 9 (02) :684-704
[5]   Global stability of humoral immunity virus dynamics models with nonlinear infection rate and removal [J].
Elaiw, A. M. ;
AlShamrani, N. H. .
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2015, 26 :161-190
[6]  
ELAIW A. M., 2014, Journal of the Korean Society for Industrial and Applied Mathematics, V18, P317, DOI 10.12941/jksiam.2014.18.317
[7]   Global properties of a class of HIV models [J].
Elaiw, A. M. .
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (04) :2253-2263
[8]  
Hattaf K., 2016, INT J DYN CONTROL, V4, P254, DOI [DOI 10.1007/S40435-015-0158-1, 10.1007/s40435-015-0158-1]
[9]   COMPLETE CLASSIFICATION OF GLOBAL DYNAMICS OF A VIRUS MODEL WITH IMMUNE RESPONSES [J].
Jiang, Cuicui ;
Wang, Wendi .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2014, 19 (04) :1087-1103
[10]  
Kuang Y., 1993, DELAY DIFFERENTIAL E