Analysis of a periodic bacteria-immunity model with delayed quorum sensing

被引：0

作者：

Zhang Zhonghua ^{[1
]}

Suo Yaohong ^{[1
]}

Peng Jigeng ^{[2
]}

Zhang Juan ^{[3
]}

机构：

[1] Xian Univ Sci & Technol, Sch Sci, Xian 710054, Peoples R China

[2] Xian Jiaotong Univ, Res Ctr Appl Math, Xian 710049, Peoples R China

[3] N China Elect Power Univ, Dept Math, Beijing 102206, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2008年 / 56卷 / 11期

关键词：

Quorum sensing; Immunity; Periodic solution; Stability; Subharmonic bifurcation; Perturbation;

D O I：

10.1016/j.camwa.2008.09.019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Based on [J. Zhang, M. Cerasuolo, P. Fergola, Z.E. Ma, On the influence of quorum sensing in the competition between bacteria and immune system (in press)], a bacteria-immunity model with periodically bacterial quorum sensing is formulated which describes the competition between bacteria and immune cells. A discrete delay is introduced to characterize the time in which bacteria receive signal molecules and combat with immune cells. In this paper, we focus on a subsystem of the bacteria-immunity model, investigate the existence and stability of the positively periodic solution, and discuss the existence of subharmonic bifurcation by the perturbation method. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：2834 / 2847

页数：14

共 12 条

[1] INHIBITION AND ACTIVATION OF BACTERIAL LUCIFERASE SYNTHESIS
EBERHARD, A
[J]. JOURNAL OF BACTERIOLOGY, 1972, 109 (03) : 1101 - &
[2] Some new results on an allelopathic competition model with quorum sensing and delayed toxicant production
Fergola, P.
Beretta, E.
Cerasuolo, M.
[J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2006, 7 (05) : 1081 - 1095
[3] Applications of Sturm sequences to bifurcation analysis of delay differential equation models
Forde, J
Nelson, P
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 300 (02) : 273 - 284
[4] Bacterial social engagements
Henke, JM
Bassler, BL
[J]. TRENDS IN CELL BIOLOGY, 2004, 14 (11) : 648 - 656
[5] The importance of the innate immune system in controlling HIV infection and disease
Levy, JA
[J]. TRENDS IN IMMUNOLOGY, 2001, 22 (06) : 312 - 316
[6] Innate immune recognition and control of adaptive immune responses
Medzhitov, R
Janeway, CA
[J]. SEMINARS IN IMMUNOLOGY, 1998, 10 (05) : 351 - 353
[7] CELLULAR CONTROL OF SYNTHESIS AND ACTIVITY OF BACTERIAL LUMINESCENT SYSTEM
NEALSON, KH
PLATT, T
HASTINGS, JW
[J]. JOURNAL OF BACTERIOLOGY, 1970, 104 (01) : 313 - &
[8] SMITH HL, 1983, J MATH BIOL, V17, P163, DOI 10.1007/BF00305757
[9] MULTIPLE STABLE SUBHARMONICS FOR A PERIODIC EPIDEMIC MODEL
SMITH, HL
[J]. JOURNAL OF MATHEMATICAL BIOLOGY, 1983, 17 (02) : 179 - 190
[10] Williams Paul, 2002, Expert Opin Ther Targets, V6, P257, DOI 10.1517/14728222.6.3.257

← 1 2 →