Complementary analysis of the initial value problem for a system of o.d.e. modelling the immune system after vaccinations

Urszula Foryś; Norbert Żołek

Applicationes Mathematicae (2000)

  • Volume: 27, Issue: 1, page 103-111
  • ISSN: 1233-7234

Abstract

top
Complementary analysis of a model of the human immune system after a series of vaccinations, proposed in [7] and studied in [6], is presented. It is shown that all coordinates of every solution have at most two extremal values. The theoretical results are compared with experimental data.

How to cite

top

Foryś, Urszula, and Żołek, Norbert. "Complementary analysis of the initial value problem for a system of o.d.e. modelling the immune system after vaccinations." Applicationes Mathematicae 27.1 (2000): 103-111. <http://eudml.org/doc/219254>.

@article{Foryś2000,
abstract = {Complementary analysis of a model of the human immune system after a series of vaccinations, proposed in [7] and studied in [6], is presented. It is shown that all coordinates of every solution have at most two extremal values. The theoretical results are compared with experimental data.},
author = {Foryś, Urszula, Żołek, Norbert},
journal = {Applicationes Mathematicae},
keywords = {VT-complex; antibody; antigen; B-cell; plasma cell; stationary state; stability; ordinary differential equations; lymphocyte; phase space},
language = {eng},
number = {1},
pages = {103-111},
title = {Complementary analysis of the initial value problem for a system of o.d.e. modelling the immune system after vaccinations},
url = {http://eudml.org/doc/219254},
volume = {27},
year = {2000},
}

TY - JOUR
AU - Foryś, Urszula
AU - Żołek, Norbert
TI - Complementary analysis of the initial value problem for a system of o.d.e. modelling the immune system after vaccinations
JO - Applicationes Mathematicae
PY - 2000
VL - 27
IS - 1
SP - 103
EP - 111
AB - Complementary analysis of a model of the human immune system after a series of vaccinations, proposed in [7] and studied in [6], is presented. It is shown that all coordinates of every solution have at most two extremal values. The theoretical results are compared with experimental data.
LA - eng
KW - VT-complex; antibody; antigen; B-cell; plasma cell; stationary state; stability; ordinary differential equations; lymphocyte; phase space
UR - http://eudml.org/doc/219254
ER -

References

top
  1. [1] L. N. Belykh, Analysis of Mathematical Models in Immunology, Nauka, Moscow, 1988 (in Russian). Zbl0663.92003
  2. [2] A. Borkowska and W. Szlenk, A mathematical model of decreasing of antibodies concentration after vaccination in the case of hepatitis B, Polish J. Immunology 20 (1995), 117-122. 
  3. [3] S. D. Cohen and A. C. Hindmarsh, CVODE, a Stiff/Nonstiff ODE Solver in C, Computers in Physics 10 (1996), no. 2. 
  4. [4] U. Foryś, Global analysis of Marchuk's model in a case of weak immune system, Math. Comput. Modelling 25 (1997), 97-106. Zbl0919.92022
  5. [5] U. Foryś, Global analysis of Marchuk's model in case of strong immune system, J. Math. Biol., to appear. 
  6. [6] U. Foryś, Global analysis of the initial value problem for a system of O.D.E. modelling the immune system after vaccinations, Math. Comput. Modelling 29 (1999), 79-85. Zbl1070.92517
  7. [7] U. Foryś and N. Żołek, A model of immune system after vaccinations, ARI 50 (1998), 180-184. 
  8. [8] M. Gesemann and N. Scheiermann, Kinetics of hepatitis B vaccine-induced anti-hbs antibodies during 82 month post-booster period, in: Proc. Internat. Sympos. Viral and Liver Disease, Tokyo, 1993, abs. 244. 
  9. [9] A. J. Hall, Immunization against viral hepatitis type B: how long protection and against what?, Brit. Med. 1994, IV 7-8. 
  10. [10] K. Madaliński, Vaccination against hepatitis B--Current status and perspectives, Polish J. Immunology 20 (1995), 3-15. 
  11. [11] G. I. Marchuk, Mathematical Models in Immunology, Optimization Software, Publ. Division, New York, 1983. Zbl0556.92006
  12. [12] G. I. Marchuk, Mathematical Modelling of Immune Response in Infectious Diseases, Kluwer Acad. Publ., Dordrecht, 1997. Zbl0876.92015

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.