Dynamical Analysis of a Delayed HIV Virus Dynamic Model with Cell-to-Cell Transmission and Apoptosis of Bystander Cells

被引：3

作者：

Zhang, Tongqian ^{[1
,2
,3
]}

Wang, Junling ^{[1
]}

Song, Yi ^{[1
]}

Jiang, Zhichao ^{[4
]}

机构：

[1] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China

[2] Shandong Univ Sci & Technol, State Key Lab Min Disaster Prevent & Control, Qingdao 266590, Peoples R China

[3] Shandong Univ Sci & Technol, Minist Sci & Technol, Qingdao 266590, Peoples R China

[4] North China Inst Aerosp Engn, Sch Liberal Arts & Sci, Langfang 065000, Peoples R China

来源：

COMPLEXITY | 2020年 / 2020卷

基金：

中国国家自然科学基金;

关键词：

CTL IMMUNE-RESPONSE; MATHEMATICAL-ANALYSIS; INFECTION MODEL; GLOBAL STABILITY; VIRAL DYNAMICS; SPREAD; TIME; CD4(+); GROWTH;

D O I：

10.1155/2020/2313102

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, a delayed viral dynamical model that considers two different transmission methods of the virus and apoptosis of bystander cells is proposed and investigated. The basic reproductive number R-0 of the model is derived. Based on the basic reproductive number, we prove that the disease-free equilibrium E-0 is globally asymptotically stable for R-0<1 by constructing suitable Lyapunov functional. For R-0>1, by regarding the time delay as bifurcation parameter, the existence of local Hopf bifurcation is investigated. The results show that time delay can change the stability of endemic equilibrium and cause periodic oscillations. Finally, we give some numerical simulations to illustrate the theoretical findings.

引用

页数：12

共 54 条

[1] The immune control and cell-to-cell spread of human T-lymphotropic virus type 1 [J].

Bangham, CRM .

JOURNAL OF GENERAL VIROLOGY, 2003, 84 :3177-3189

[2] A SINGULARLY PERTURBED HIV MODEL WITH TREATMENT AND ANTIGENIC VARIATION [J].

Bobko, Nara ;

Zubelli, Jorge P. .

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 2015, 12 (01) :1-21

[3] A CLASS OF VIRUS DYNAMIC MODEL WITH INHIBITORY EFFECT ON THE GROWTH OF UNINFECTED T CELLS CAUSED BY INFECTED T CELLS AND ITS STABILITY ANALYSIS [J].

Cheng, Wenbo ;

Ma, Wanbiao ;

Guo, Songbai .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2016, 15 (03) :795-806

[4] Apoptosis of CD4(+) and CD8(+) T cells isolated immediately ex vivo correlates with disease severity in human immunodeficiency virus Type 1 infection [J].

Cotton, MF ;

Ikle, DN ;

Rapaport, EL ;

Marschner, S ;

Tseng, PO ;

Kurrle, R ;

Finkel, TH .

PEDIATRIC RESEARCH, 1997, 42 (05) :656-664

[5] A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay [J].

Culshaw, RV ;

Ruan, SG ;

Webb, G .

JOURNAL OF MATHEMATICAL BIOLOGY, 2003, 46 (05) :425-444

[6] Analysis of a stochastic HIV-1 infection model with degenerate diffusion [J].

Feng, Tao ;

Qiu, Zhipeng ;

Meng, Xinzhu ;

Rong, Libin .

APPLIED MATHEMATICS AND COMPUTATION, 2019, 348 :437-455

[7] APOPTOSIS OCCURS PREDOMINANTLY IN BYSTANDER CELLS AND NOT IN PRODUCTIVELY INFECTED-CELLS OF HIV-INFECTED AND SIV-INFECTED LYMPH-NODES [J].

FINKEL, TH ;

TUDORWILLIAMS, G ;

BANDA, NK ;

COTTON, MF ;

CURIEL, T ;

MONKS, C ;

BABA, TW ;

RUPRECHT, RM ;

KUPFER, A .

NATURE MEDICINE, 1995, 1 (02) :129-134

[8] GLOBAL BEHAVIOR OF DELAY DIFFERENTIAL EQUATIONS MODEL OF HIV INFECTION WITH APOPTOSIS [J].

Guo, Songbai ;

Ma, Wanbiao .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2016, 21 (01) :103-119

[9] Modeling the role of macrophages in HIV persistence during antiretroviral therapy [J].

Guo, Ting ;

Qiu, Zhipeng ;

Rong, Libin .

JOURNAL OF MATHEMATICAL BIOLOGY, 2020, 81 (01) :369-402

[10] A within-host drug resistance model with continuous state-dependent viral strains [J].

Guo, Ting ;

Qiu, Zhipeng ;

Rong, Libin .

APPLIED MATHEMATICS LETTERS, 2020, 104

← 1 2 3 4 5 6 →