Modeling the interaction of cytotoxic T lymphocytes and influenza
virus infected epithelial cells
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1.
Applied Sciences and Mathematics Department, Arizona State University at the Polytechnic campus, Mesa, Arizona, 85212
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2.
School of Mathematics and Statistical Sciences, Arizona State University, Tempe, AZ 85281
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Received:
01 July 2009
Accepted:
29 June 2018
Published:
01 January 2010
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MSC :
Primary: 34K20, 92C50; Secondary: 92D25.
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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 influenzavirus infected epithelial cells[J]. Mathematical Biosciences and Engineering, 2010, 7(1): 171-185. doi: 10.3934/mbe.2010.7.171
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Abstract
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.
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