# American Institute of Mathematical Sciences

2010, 7(1): 171-185. doi: 10.3934/mbe.2010.7.171

## Modeling the interaction of cytotoxic T lymphocytes and influenza virus infected epithelial cells

 1 Applied Sciences and Mathematics Department, Arizona State University at the Polytechnic campus, Mesa, Arizona, 85212, United States 2 School of Mathematics and Statistical Sciences, Arizona State University, Tempe, AZ 85281, United States

Received  July 2009 Revised  November 2009 Published  January 2010

The aim of this work is to investigate the mechanisms involved in the clearance of viral infection of the influenza virus at the epithelium level by modeling and analyzing the interaction of the influenza virus specific cytotoxic T Lymphocytes (CTL cells) and the influenza virus infected epithelial cells. Since detailed and definite mechanisms that trigger CTL production and cell death are still debatable, we utilize two plausible mathematical models for the CTLs response to influenza infection (i) logistic growth and (ii) threshold growth. These models incorporate the simulating effect of the production of CTLs during the infection. The systematical analysis of these models show that the behaviors of the models are similar when CTL density is high and in which case both generate reasonable dynamics. However, both models failed to produce the desirable and natural clearance dynamic. Nevertheless, at lower CTL density, the threshold model shows the possibility of existence of a "lower" equilibrium. This sub-threshold equilibrium may represent dose-dependent immune response to low level infection.
Citation: Abdessamad Tridane, Yang Kuang. Modeling the interaction of cytotoxic T lymphocytes and influenza virus infected epithelial cells. Mathematical Biosciences & Engineering, 2010, 7 (1) : 171-185. doi: 10.3934/mbe.2010.7.171
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