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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: wwwzhonghua@sohu.com
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
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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

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