Skip to main content Accessibility help
×
Home

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

  • Zhonghua Zhang (a1), Juan Zhang (a2) and Jigeng Peng (a3)

Extract

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.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

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

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

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

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

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

Copyright

References

Hide All
[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), 3983.
[2]Eberhard, A., ‘Inhibition and activation of bacterial liuciferase synthesis’, J. Bacteriol. 109 (1972), 11011105.
[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), 10811095.
[4]Gaines, R.I. and Mawhin, J.L., Coincidence degree, and nonlinear differential equations (Springer-Verlag, Berlin, 1977).
[5]Henke, J.M. and Bassler, B.L., ‘Bacterial social engagements’, Trends in Cell Biology 14 (2004), 648656.
[6]Levy, J.A., ‘The importance of the innate immune system in controlling HIV infection and disease’, Trends of Immunology 22 (2001), 312316.
[7]Medzhitov, R. and Janeway, C.A. Jr., ‘Innate immune recognition and control of adaptive immune responses’, Seminars in Immunology 10 (1998), 351353.
[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), 313322.
[9]Slotine, J.J.E. and Li, W., Applied nonlinear contro (Prentice-Hall, Englewood Cliffs, NJ, 1991).
[10]Williams, P., ‘Quorum sensing: an emerging target for antibacterial chemotherapy?’, Expert. Opin. Ther. Target 6 (2002), 257274.
[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).
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

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

  • Zhonghua Zhang (a1), Juan Zhang (a2) and Jigeng Peng (a3)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed