American Institute of Mathematical Sciences

Advanced
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

Abdessamad Tridane 1, and  Yang Kuang 2,

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.
Keywords: cytotoxic T lymphocytes, immune response, influenza virus, mathematical model..
Mathematics Subject Classification: Primary: 34K20, 92C50; Secondary: 92D2.
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
[1]

Haitao Song, Weihua Jiang, Shengqiang Liu. Virus dynamics model with intracellular delays and immune response. Mathematical Biosciences & Engineering, 2015, 12 (1) : 185-208. doi: 10.3934/mbe.2015.12.185
[2]

Cameron Browne. Immune response in virus model structured by cell infection-age. Mathematical Biosciences & Engineering, 2016, 13 (5) : 887-909. doi: 10.3934/mbe.2016022
[3]

Marcello Delitala, Tommaso Lorenzi. Recognition and learning in a mathematical model for immune response against cancer. Discrete & Continuous Dynamical Systems - B, 2013, 18 (4) : 891-914. doi: 10.3934/dcdsb.2013.18.891
[4]

Loïc Barbarroux, Philippe Michel, Mostafa Adimy, Fabien Crauste. A multiscale model of the CD8 T cell immune response structured by intracellular content. Discrete & Continuous Dynamical Systems - B, 2018, 23 (9) : 3969-4002. doi: 10.3934/dcdsb.2018120
[5]

Yueping Dong, Rinko Miyazaki, Yasuhiro Takeuchi. Mathematical modeling on helper T cells in a tumor immune system. Discrete & Continuous Dynamical Systems - B, 2014, 19 (1) : 55-72. doi: 10.3934/dcdsb.2014.19.55
[6]

Cuicui Jiang, Kaifa Wang, Lijuan Song. Global dynamics of a delay virus model with recruitment and saturation effects of immune responses. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 1233-1246. doi: 10.3934/mbe.2017063
[7]

Cuicui Jiang, Wendi Wang. Complete classification of global dynamics of a virus model with immune responses. Discrete & Continuous Dynamical Systems - B, 2014, 19 (4) : 1087-1103. doi: 10.3934/dcdsb.2014.19.1087
[8]

Mohammad A. Tabatabai, Wayne M. Eby, Karan P. Singh, Sejong Bae. T model of growth and its application in systems of tumor-immune dynamics. Mathematical Biosciences & Engineering, 2013, 10 (3) : 925-938. doi: 10.3934/mbe.2013.10.925
[9]

Sumei Li, Yicang Zhou. Backward bifurcation of an HTLV-I model with immune response. Discrete & Continuous Dynamical Systems - B, 2016, 21 (3) : 863-881. doi: 10.3934/dcdsb.2016.21.863
[10]

Fabrizio Clarelli, Roberto Natalini. A pressure model of immune response to mycobacterium tuberculosis infection in several space dimensions. Mathematical Biosciences & Engineering, 2010, 7 (2) : 277-300. doi: 10.3934/mbe.2010.7.277
[11]

Seema Nanda, Lisette dePillis, Ami Radunskaya. B cell chronic lymphocytic leukemia - A model with immune response. Discrete & Continuous Dynamical Systems - B, 2013, 18 (4) : 1053-1076. doi: 10.3934/dcdsb.2013.18.1053
[12]

Louis D. Bergsman, James M. Hyman, Carrie A. Manore. A mathematical model for the spread of west nile virus in migratory and resident birds. Mathematical Biosciences & Engineering, 2016, 13 (2) : 401-424. doi: 10.3934/mbe.2015009
[13]

Wenbo Cheng, Wanbiao Ma, Songbai Guo. A class of virus dynamic model with inhibitory effect on the growth of uninfected T cells caused by infected T cells and its stability analysis. Communications on Pure & Applied Analysis, 2016, 15 (3) : 795-806. doi: 10.3934/cpaa.2016.15.795
[14]

J.C. Arciero, T.L. Jackson, D.E. Kirschner. A mathematical model of tumor-immune evasion and siRNA treatment. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 39-58. doi: 10.3934/dcdsb.2004.4.39
[15]

Kaifa Wang, Yu Jin, Aijun Fan. The effect of immune responses in viral infections: A mathematical model view. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : 3379-3396. doi: 10.3934/dcdsb.2014.19.3379
[16]

D. Criaco, M. Dolfin, L. Restuccia. Approximate smooth solutions of a mathematical model for the activation and clonal expansion of T cells. Mathematical Biosciences & Engineering, 2013, 10 (1) : 59-73. doi: 10.3934/mbe.2013.10.59
[17]

Alan D. Rendall. Multiple steady states in a mathematical model for interactions between T cells and macrophages. Discrete & Continuous Dynamical Systems - B, 2013, 18 (3) : 769-782. doi: 10.3934/dcdsb.2013.18.769
[18]

Urszula Ledzewicz, Mozhdeh Sadat Faraji Mosalman, Heinz Schättler. Optimal controls for a mathematical model of tumor-immune interactions under targeted chemotherapy with immune boost. Discrete & Continuous Dynamical Systems - B, 2013, 18 (4) : 1031-1051. doi: 10.3934/dcdsb.2013.18.1031
[19]

Jinliang Wang, Lijuan Guan. Global stability for a HIV-1 infection model with cell-mediated immune response and intracellular delay. Discrete & Continuous Dynamical Systems - B, 2012, 17 (1) : 297-302. doi: 10.3934/dcdsb.2012.17.297
[20]

Hee-Dae Kwon, Jeehyun Lee, Myoungho Yoon. An age-structured model with immune response of HIV infection: Modeling and optimal control approach. Discrete & Continuous Dynamical Systems - B, 2014, 19 (1) : 153-172. doi: 10.3934/dcdsb.2014.19.153

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (19)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences