-
Previous Article
Dynamical analysis in growth models: Blumberg's equation
- DCDS-B Home
- This Issue
-
Next Article
Adaptation and migration of a population between patches
Multiple steady states in a mathematical model for interactions between T cells and macrophages
1. | Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, 14476 Potsdam, Germany |
References:
[1] |
R. Callard, Decision-making by the immune response, Immun. and Cell Biol., 85 (2007), 300-305. |
[2] |
R. de Waal Malefyt, J. Haanen, H. Spits, M.-G. Roncarolo, A. te Velde, C. Figdor, K. Johnson, R. Kastelein, H. Yssel and J. E. de Vries, Interleukin 10 (IL-10) and viral IL-10 strongly reduce antigen-specific human T cell proliferation by diminishing the antigen-presenting capacity of monocytes via downregulation of Class II major histocompatibility complex expression, J. Exp. Med., 174 (1991), 915-924. |
[3] |
M. W. Hirsch, Systems of differential equations which are competitive or cooperative. I: Limit sets, SIAM J. Math. Anal., 13 (1982), 167-179.
doi: 10.1137/0513013. |
[4] |
E. Klipp, R. Herwig, A. Kowald, C. Wierling and H. Lehrach, "Systems Biology in Practice," Wiley-VCH, Weinheim, 2005. |
[5] |
R. Lev Bar-Or, Feedback mechanisms between T helper cells and macrophages in the determination of the immune response, Math. Biosci., 163 (2000), 35-58. |
[6] |
R. M. May, Uses and abuses of mathematics in biology, Science, 303 (2004), 790-793. |
[7] |
K. M. Murphy, P. Travers and M. Walport, "Janeway's Immunobiology," Garland Science, New York, 2007. |
[8] |
A. D. Rendall, Analysis of a mathematical model for interactions between T cells and macrophages, Electr. J. Diff. Eq., 2010 (2010), 115. |
[9] |
I. Roitt, J. Brostoff, D. Male and D. Roth, "Immunology," Mosby, New York, 2006. |
[10] |
L. Steinman, A brief history of Th17, the first major revision of the Th1/Th2 hypothesis of T cell-mediated tissue damage, Nature Med., 13 (2007), 139-145. |
[11] |
H.-J. van den Hamm and R. J. de Boer, From the two-dimensional Th1 and Th2 phenotypes to high-dimensional models for gene regulation, Int. Immunol., 20 (2008), 1269-1277. |
[12] |
A. Yates, R. Callard and J. Stark, Combining cytokine signalling with T-bet and GATA-3 regulation in Th1 and Th2 differentiation: A model for cellular decision-making, J. Theor. Biol., 231 (2004), 181-196.
doi: 10.1016/j.jtbi.2004.06.013. |
show all references
References:
[1] |
R. Callard, Decision-making by the immune response, Immun. and Cell Biol., 85 (2007), 300-305. |
[2] |
R. de Waal Malefyt, J. Haanen, H. Spits, M.-G. Roncarolo, A. te Velde, C. Figdor, K. Johnson, R. Kastelein, H. Yssel and J. E. de Vries, Interleukin 10 (IL-10) and viral IL-10 strongly reduce antigen-specific human T cell proliferation by diminishing the antigen-presenting capacity of monocytes via downregulation of Class II major histocompatibility complex expression, J. Exp. Med., 174 (1991), 915-924. |
[3] |
M. W. Hirsch, Systems of differential equations which are competitive or cooperative. I: Limit sets, SIAM J. Math. Anal., 13 (1982), 167-179.
doi: 10.1137/0513013. |
[4] |
E. Klipp, R. Herwig, A. Kowald, C. Wierling and H. Lehrach, "Systems Biology in Practice," Wiley-VCH, Weinheim, 2005. |
[5] |
R. Lev Bar-Or, Feedback mechanisms between T helper cells and macrophages in the determination of the immune response, Math. Biosci., 163 (2000), 35-58. |
[6] |
R. M. May, Uses and abuses of mathematics in biology, Science, 303 (2004), 790-793. |
[7] |
K. M. Murphy, P. Travers and M. Walport, "Janeway's Immunobiology," Garland Science, New York, 2007. |
[8] |
A. D. Rendall, Analysis of a mathematical model for interactions between T cells and macrophages, Electr. J. Diff. Eq., 2010 (2010), 115. |
[9] |
I. Roitt, J. Brostoff, D. Male and D. Roth, "Immunology," Mosby, New York, 2006. |
[10] |
L. Steinman, A brief history of Th17, the first major revision of the Th1/Th2 hypothesis of T cell-mediated tissue damage, Nature Med., 13 (2007), 139-145. |
[11] |
H.-J. van den Hamm and R. J. de Boer, From the two-dimensional Th1 and Th2 phenotypes to high-dimensional models for gene regulation, Int. Immunol., 20 (2008), 1269-1277. |
[12] |
A. Yates, R. Callard and J. Stark, Combining cytokine signalling with T-bet and GATA-3 regulation in Th1 and Th2 differentiation: A model for cellular decision-making, J. Theor. Biol., 231 (2004), 181-196.
doi: 10.1016/j.jtbi.2004.06.013. |
[1] |
Zaki Chbani, Hassan Riahi. Existence and asymptotic behaviour for solutions of dynamical equilibrium systems. Evolution Equations and Control Theory, 2014, 3 (1) : 1-14. doi: 10.3934/eect.2014.3.1 |
[2] |
Dorothy Bollman, Omar Colón-Reyes. Determining steady state behaviour of discrete monomial dynamical systems. Advances in Mathematics of Communications, 2017, 11 (2) : 283-287. doi: 10.3934/amc.2017019 |
[3] |
Stephen C. Anco, Elena Recio. Accelerating dynamical peakons and their behaviour. Discrete and Continuous Dynamical Systems, 2019, 39 (10) : 6131-6148. doi: 10.3934/dcds.2019267 |
[4] |
Aicha Balhag, Zaki Chbani, Hassan Riahi. Existence and continuous-discrete asymptotic behaviour for Tikhonov-like dynamical equilibrium systems. Evolution Equations and Control Theory, 2018, 7 (3) : 373-401. doi: 10.3934/eect.2018019 |
[5] |
Jianfeng Feng, Mariya Shcherbina, Brunello Tirozzi. Dynamical behaviour of a large complex system. Communications on Pure and Applied Analysis, 2008, 7 (2) : 249-265. doi: 10.3934/cpaa.2008.7.249 |
[6] |
Igor Chueshov, Björn Schmalfuss. Qualitative behavior of a class of stochastic parabolic PDEs with dynamical boundary conditions. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 315-338. doi: 10.3934/dcds.2007.18.315 |
[7] |
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 |
[8] |
Neville J. Ford, Stewart J. Norton. Predicting changes in dynamical behaviour in solutions to stochastic delay differential equations. Communications on Pure and Applied Analysis, 2006, 5 (2) : 367-382. doi: 10.3934/cpaa.2006.5.367 |
[9] |
Shohel Ahmed, Abdul Alim, Sumaiya Rahman. A controlled treatment strategy applied to HIV immunology model. Numerical Algebra, Control and Optimization, 2018, 8 (3) : 299-314. doi: 10.3934/naco.2018019 |
[10] |
El Houcein El Abdalaoui, Sylvain Bonnot, Ali Messaoudi, Olivier Sester. On the Fibonacci complex dynamical systems. Discrete and Continuous Dynamical Systems, 2016, 36 (5) : 2449-2471. doi: 10.3934/dcds.2016.36.2449 |
[11] |
Lianfa He, Hongwen Zheng, Yujun Zhu. Shadowing in random dynamical systems. Discrete and Continuous Dynamical Systems, 2005, 12 (2) : 355-362. doi: 10.3934/dcds.2005.12.355 |
[12] |
Mauricio Achigar. Extensions of expansive dynamical systems. Discrete and Continuous Dynamical Systems, 2021, 41 (7) : 3093-3108. doi: 10.3934/dcds.2020399 |
[13] |
Fritz Colonius, Marco Spadini. Fundamental semigroups for dynamical systems. Discrete and Continuous Dynamical Systems, 2006, 14 (3) : 447-463. doi: 10.3934/dcds.2006.14.447 |
[14] |
John Erik Fornæss. Sustainable dynamical systems. Discrete and Continuous Dynamical Systems, 2003, 9 (6) : 1361-1386. doi: 10.3934/dcds.2003.9.1361 |
[15] |
Vieri Benci, C. Bonanno, Stefano Galatolo, G. Menconi, M. Virgilio. Dynamical systems and computable information. Discrete and Continuous Dynamical Systems - B, 2004, 4 (4) : 935-960. doi: 10.3934/dcdsb.2004.4.935 |
[16] |
Mădălina Roxana Buneci. Morphisms of discrete dynamical systems. Discrete and Continuous Dynamical Systems, 2011, 29 (1) : 91-107. doi: 10.3934/dcds.2011.29.91 |
[17] |
Josiney A. Souza, Tiago A. Pacifico, Hélio V. M. Tozatti. A note on parallelizable dynamical systems. Electronic Research Announcements, 2017, 24: 64-67. doi: 10.3934/era.2017.24.007 |
[18] |
Philippe Marie, Jérôme Rousseau. Recurrence for random dynamical systems. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 1-16. doi: 10.3934/dcds.2011.30.1 |
[19] |
Tobias Wichtrey. Harmonic limits of dynamical systems. Conference Publications, 2011, 2011 (Special) : 1432-1439. doi: 10.3934/proc.2011.2011.1432 |
[20] |
Kolade M. Owolabi. Dynamical behaviour of fractional-order predator-prey system of Holling-type. Discrete and Continuous Dynamical Systems - S, 2020, 13 (3) : 823-834. doi: 10.3934/dcdss.2020047 |
2021 Impact Factor: 1.497
Tools
Metrics
Other articles
by authors
[Back to Top]