American Institute of Mathematical Sciences

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July  2007, 8(1): 241-259. doi: 10.3934/dcdsb.2007.8.241

Immune system memory realization in a population model

Jianhong Wu 1, , Weiguang Yao 2, and  Huaiping Zhu 3,

1. 

Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3
2. 

LAboratory of Mathematical Parallel systems (LAMPS), Laboratory for Industrial and Applied Mathematics (LIAM), Department of Mathematics and Statistics, York University, Toronto M3J 1P3, Canada
3. 

Department of Mathematics and Statistics, Laboratory of Mathematical Parallel systems (LAMPS) and CDM, York University, Toronto M3J 1P3, Canada

Received  December 2005 Revised  October 2006 Published  April 2007

A general process of the immune system consists of effector stage and memory stage. Current theoretical studies of the immune system often focus on the memory stage and pay less attention on the function of non-immune system substances such as tissue cells in adjusting the dynamical behavior of the immune system. We propose a mathematical population model to investigate the interaction between influenza A virus(IAV) susceptible tissue cells and generic immune cells when the tissue is invaded by IAV. We carry out a linear stability analysis and numerically study the Neimark-Sacker bifurcation of the models. The behavior of the model system agrees with some important experimental or clinical observations for IAV. However, we show that without considering the space between tissue cells, the expected memory stage does not form. By considering the space which allows antibodies to bind antigens, the memory stage then forms without missing the property of the system in the effector stage.
Keywords: age-dependent mathematical model., IAV, memory stage, Immune system, effector stage.
Mathematics Subject Classification: Primary: 92D; Secondary: 34K11, 37N2.
Citation: Jianhong Wu, Weiguang Yao, Huaiping Zhu. Immune system memory realization in a population model. Discrete and Continuous Dynamical Systems - B, 2007, 8 (1) : 241-259. doi: 10.3934/dcdsb.2007.8.241
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