American Institute of Mathematical Sciences

Advanced
September  2009, 12(2): 323-336. doi: 10.3934/dcdsb.2009.12.323

A preliminary mathematical model of skin dendritic cell trafficking and induction of T cell immunity

Amy H. Lin Erickson 1, , Alison Wise 2, , Stephen Fleming 3, , Margaret Baird 3, , Zabeen Lateef 3, , Annette Molinaro 4, , Miranda Teboh-Ewungkem 5, and  Lisette dePillis 6,

1. 

Georgia Gwinnett College, Lawrenceville, GA 30043, United States
2. 

Department of Biostatistics, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States
3. 

Department of Microbiology and Immunology, University of Otago, Dunedin, 9054, New Zealand, New Zealand, New Zealand
4. 

Biostatistics Division, Yale University, New Haven, CT 06520, United States
5. 

Department of Mathematics, Lafayette College, Easton, PA 18042, United States
6. 

Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, United States

Received  September 2008 Revised  April 2009 Published  July 2009

Chronic inflammation is a process where dendritic cells (DCs) are constantly sampling antigen in the skin and migrating to lymph nodes where they induce the activation and proliferation of T cells. The T cells then travel back to the skin where they release cytokines that induce/maintain the inflammatory condition. This process is cyclic and ongoing. We created a differential equations model to reflect the initial stages of the inflammatory process. In particular, we modeled antigen stimulation of DCs in the skin, movement of DCs from the skin to a lymph node, and the subsequent activation of T cells in the lymph node. The model was able to simulate DC and T cell responses to antigen introduction taking place within realistic time scales. The goal of such a preliminary model is simply to be able to capture biologically realistic dynamics. Future models can then build on this preliminary model in directions that can potentially allow not only for model validation, but for predictions and hypothesis testing.
Keywords: antigen, Dendritic cells, differential equations, immunology modeling..
Mathematics Subject Classification: Primary: 92C50; Secondary: 92B0.
Citation: Amy H. Lin Erickson, Alison Wise, Stephen Fleming, Margaret Baird, Zabeen Lateef, Annette Molinaro, Miranda Teboh-Ewungkem, Lisette dePillis. A preliminary mathematical model of skin dendritic cell trafficking and induction of T cell immunity. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 323-336. doi: 10.3934/dcdsb.2009.12.323
[1]

Maria Vittoria Barbarossa, Christina Kuttler, Jonathan Zinsl. Delay equations modeling the effects of phase-specific drugs and immunotherapy on proliferating tumor cells. Mathematical Biosciences & Engineering, 2012, 9 (2) : 241-257. doi: 10.3934/mbe.2012.9.241
[2]

Robert P. Gilbert, Philippe Guyenne, Ying Liu. Modeling of the kinetics of vitamin D$_3$ in osteoblastic cells. Mathematical Biosciences & Engineering, 2013, 10 (2) : 319-344. doi: 10.3934/mbe.2013.10.319
[3]

Thierry Colin, Marie-Christine Durrieu, Julie Joie, Yifeng Lei, Youcef Mammeri, Clair Poignard, Olivier Saut. Modeling of the migration of endothelial cells on bioactive micropatterned polymers. Mathematical Biosciences & Engineering, 2013, 10 (4) : 997-1015. doi: 10.3934/mbe.2013.10.997
[4]

Stéphane Junca, Bruno Lombard. Stability of neutral delay differential equations modeling wave propagation in cracked media. Conference Publications, 2015, 2015 (special) : 678-685. doi: 10.3934/proc.2015.0678
[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]

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
[7]

Junde Wu, Shangbin Cui. Asymptotic behavior of solutions for parabolic differential equations with invariance and applications to a free boundary problem modeling tumor growth. Discrete & Continuous Dynamical Systems - A, 2010, 26 (2) : 737-765. doi: 10.3934/dcds.2010.26.737
[8]

Eduardo Ibarguen-Mondragon, Lourdes Esteva, Leslie Chávez-Galán. A mathematical model for cellular immunology of tuberculosis. Mathematical Biosciences & Engineering, 2011, 8 (4) : 973-986. doi: 10.3934/mbe.2011.8.973
[9]

Bertrand Maury, Aude Roudneff-Chupin, Filippo Santambrogio. Congestion-driven dendritic growth. Discrete & Continuous Dynamical Systems - A, 2014, 34 (4) : 1575-1604. doi: 10.3934/dcds.2014.34.1575
[10]

Shohel Ahmed, Abdul Alim, Sumaiya Rahman. A controlled treatment strategy applied to HIV immunology model. Numerical Algebra, Control & Optimization, 2018, 8 (3) : 299-314. doi: 10.3934/naco.2018019
[11]

Loïs Boullu, Mostafa Adimy, Fabien Crauste, Laurent Pujo-Menjouet. Oscillations and asymptotic convergence for a delay differential equation modeling platelet production. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2417-2442. doi: 10.3934/dcdsb.2018259
[12]

Miriam Manoel, Patrícia Tempesta. Binary differential equations with symmetries. Discrete & Continuous Dynamical Systems - A, 2019, 39 (4) : 1957-1974. doi: 10.3934/dcds.2019082
[13]

Rinaldo M. Colombo, Thomas Lorenz, Nikolay I. Pogodaev. On the modeling of moving populations through set evolution equations. Discrete & Continuous Dynamical Systems - A, 2015, 35 (1) : 73-98. doi: 10.3934/dcds.2015.35.73
[14]

S. M. Crook, M. Dur-e-Ahmad, S. M. Baer. A model of activity-dependent changes in dendritic spine density and spine structure. Mathematical Biosciences & Engineering, 2007, 4 (4) : 617-631. doi: 10.3934/mbe.2007.4.617
[15]

Joanna R. Wares, Joseph J. Crivelli, Chae-Ok Yun, Il-Kyu Choi, Jana L. Gevertz, Peter S. Kim. Treatment strategies for combining immunostimulatory oncolytic virus therapeutics with dendritic cell injections. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1237-1256. doi: 10.3934/mbe.2015.12.1237
[16]

Huaiyu Jian, Xiaolin Liu, Hongjie Ju. The regularity for a class of singular differential equations. Communications on Pure & Applied Analysis, 2013, 12 (3) : 1307-1319. doi: 10.3934/cpaa.2013.12.1307
[17]

Tomás Caraballo, Gábor Kiss. Attractivity for neutral functional differential equations. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1793-1804. doi: 10.3934/dcdsb.2013.18.1793
[18]

Michael Dellnitz, Mirko Hessel-Von Molo, Adrian Ziessler. On the computation of attractors for delay differential equations. Journal of Computational Dynamics, 2016, 3 (1) : 93-112. doi: 10.3934/jcd.2016005
[19]

Ludwig Arnold, Igor Chueshov. Cooperative random and stochastic differential equations. Discrete & Continuous Dynamical Systems - A, 2001, 7 (1) : 1-33. doi: 10.3934/dcds.2001.7.1
[20]

Ulrike Kant, Werner M. Seiler. Singularities in the geometric theory of differential equations. Conference Publications, 2011, 2011 (Special) : 784-793. doi: 10.3934/proc.2011.2011.784

2018 Impact Factor: 1.008

Tools

Metrics

  • PDF downloads (26)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences