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

• Autorzy: Urszula Foryś , Norbert S. Żołek
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

VT-complex   antibody   antigen   B-cell   plasma cell   stationary state   stability   ordinary differential equations   lymphocyte   phase space  

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2000
• Tom: 27
• Numer: 1
• Strony: 103-111

Daty

wydano

2000

otrzymano

1999-01-15

poprawiono

1999-05-06

Twórcy

autor

Urszula Foryś

• Department of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

autor

Norbert S. Żołek

• Institute of Biocybernetics and, Biomedical Engineering, Trojdena 4, 02-109 Warszawa, Poland

Bibliografia

• [1] L. N. Belykh, Analysis of Mathematical Models in Immunology, Nauka, Moscow, 1988 (in Russian).
• [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] S. D. Cohen and A. C. Hindmarsh, CVODE, a Stiff/Nonstiff ODE Solver in C, Computers in Physics 10 (1996), no. 2.
• [4] U. Foryś, Global analysis of Marchuk's model in a case of weak immune system, Math. Comput. Modelling 25 (1997), 97-106.
• [5] U. Foryś, Global analysis of Marchuk's model in case of strong immune system, J. Math. Biol., to appear.
• [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.
• [7] U. Foryś and N. Żołek, A model of immune system after vaccinations, ARI 50 (1998), 180-184.
• [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] A. J. Hall, Immunization against viral hepatitis type B: how long protection and against what?, Brit. Med. 1994, IV 7-8.
• [10] K. Madaliński, Vaccination against hepatitis B--Current status and perspectives, Polish J. Immunology 20 (1995), 3-15.
• [11] G. I. Marchuk, Mathematical Models in Immunology, Optimization Software, Publ. Division, New York, 1983.
• [12] G. I. Marchuk, Mathematical Modelling of Immune Response in Infectious Diseases, Kluwer Acad. Publ., Dordrecht, 1997.