Complementary analysis of the initial value problem for a system of o.d.e. modelling the immune system after vaccinations
Foryś, Urszula ; Żołek, Norbert
Applicationes Mathematicae, Tome 27 (2000), p. 103-111 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:219254 
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Foryś, Urszula; Żołek, Norbert. Complementary analysis of the initial value problem for a system of o.d.e. modelling the immune system after vaccinations. Applicationes Mathematicae, Tome 27 (2000) pp. 103-111. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv27i1p103bwm/

[000] [1] L. N. Belykh, Analysis of Mathematical Models in Immunology, Nauka, Moscow, 1988 (in Russian). | Zbl 0663.92003

[001] [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.

[002] [3] S. D. Cohen and A. C. Hindmarsh, CVODE, a Stiff/Nonstiff ODE Solver in C, Computers in Physics 10 (1996), no. 2.

[003] [4] U. Foryś, Global analysis of Marchuk's model in a case of weak immune system, Math. Comput. Modelling 25 (1997), 97-106. | Zbl 0919.92022

[004] [5] U. Foryś, Global analysis of Marchuk's model in case of strong immune system, J. Math. Biol., to appear.

[005] [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. | Zbl 1070.92517

[006] [7] U. Foryś and N. Żołek, A model of immune system after vaccinations, ARI 50 (1998), 180-184.

[007] [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.

[008] [9] A. J. Hall, Immunization against viral hepatitis type B: how long protection and against what?, Brit. Med. 1994, IV 7-8.

[009] [10] K. Madaliński, Vaccination against hepatitis B--Current status and perspectives, Polish J. Immunology 20 (1995), 3-15.

[010] [11] G. I. Marchuk, Mathematical Models in Immunology, Optimization Software, Publ. Division, New York, 1983. | Zbl 0556.92006

[011] [12] G. I. Marchuk, Mathematical Modelling of Immune Response in Infectious Diseases, Kluwer Acad. Publ., Dordrecht, 1997. | Zbl 0876.92015