Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-06T09:46:15.689Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  17 April 2009

Zhonghua Zhang ,
Juan Zhang  and
Jigeng Peng
Zhonghua Zhang
Affiliation:
Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, China e-mail: [email protected]
Juan Zhang
Affiliation:
Research Center for Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, China
Jigeng Peng
Affiliation:
Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, China
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Based on the work of Fergola, Zhang and Cerasuolo, a bacteria-immunity model with the mechanism of periodic quorum sensing is formulated, which describes the competition between bacteria and immune cells. A discrete delay is introduced to characterise the time between when bacteria receive signal molecules and then combat with immune cells. In this paper, we focus on a subsystem of the bacteria-immunity model and investigate the existence of a positively periodic solution, and then study its global stability.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 76 , Issue 3 , December 2007 , pp. 337 - 351
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Anguige, K., King, J.R., Ward, J.P. and Williams, P., ‘Mathematical modelling of therapies targeted at bacterial quorum sensing’, Math. Biosci. 192 (2004), 39–83.Google Scholar
[2]Eberhard, A., ‘Inhibition and activation of bacterial liuciferase synthesis’, J. Bacteriol. 109 (1972), 1101–1105.CrossRefGoogle ScholarPubMed
[3]Fergola, P., Beretta, E. and Cerasuolo, M., ‘Some new results on an allelopathic competition model with quorum sensing and delayed toxicant production’, Nonlinear Anal. Real World Appl. 7 (2006), 1081–1095.CrossRefGoogle Scholar
[4]Gaines, R.I. and Mawhin, J.L., Coincidence degree, and nonlinear differential equations (Springer-Verlag, Berlin, 1977).Google Scholar
[5]Henke, J.M. and Bassler, B.L., ‘Bacterial social engagements’, Trends in Cell Biology 14 (2004), 648–656.CrossRefGoogle ScholarPubMed
[6]Levy, J.A., ‘The importance of the innate immune system in controlling HIV infection and disease’, Trends of Immunology 22 (2001), 312–316.Google Scholar
[7]Medzhitov, R. and Janeway, C.A. Jr., ‘Innate immune recognition and control of adaptive immune responses’, Seminars in Immunology 10 (1998), 351–353.CrossRefGoogle ScholarPubMed
[8]Nealson, K.H., Platt, T. and Hastings, J.W., ‘Cellular control of the syntesis and activity of the bacterial luminescent system’, J. Bacteriol 104 (1970), 313–322.Google Scholar
[9]Slotine, J.J.E. and Li, W., Applied nonlinear contro (Prentice-Hall, Englewood Cliffs, NJ, 1991).Google Scholar
[10]Williams, P., ‘Quorum sensing: an emerging target for antibacterial chemotherapy?’, Expert. Opin. Ther. Target 6 (2002), 257–274.Google Scholar
[11]Zhang, J., Cerasuolo, M., Fergola, P. and Ma, Z., ‘On the influence of quorum sensing in the competition between bacteria and immune system’ (to appear).Google Scholar