Modele matematyczne w epidemiologii i immunologii

• Autorzy: Foryś U.

Identyfikatory

DOI

10.14708/ma.v28i42/01.1879

Warianty tytułu

EN

Mathematical models in epidemiology and immunology

• Języki publikacji: PL

Słowa kluczowe

PL

model matematyczny; modelowanie infekcji; model Marczuka; immunologia; epidemiologia

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Matematyka Stosowana : matematyka dla społeczeństwa
• Rocznik: 2000
• Tom: Nr 1
• Strony: 35--67
• Opis fizyczny: wykr., bibliogr. 45 poz.

Twórcy

autor

Foryś U.

• Instytut Matematyki Stosowanej i Mechaniki, Wydział Matematyki, Informatyki i Mechaniki Uniwersytet Warszawski, Banacha 2, 02-097 Warszawa

• Instytut Matematyki Stosowanej i Mechaniki, Wydział Matematyki, Informatyki i Mechaniki Uniwersytet Warszawski, Banacha 2, 02-097 Warszawa,

Bibliografia

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• [Bs2] I. Barradas, Immunological barrier for infectious diseases, preprint, CINVE- STAV, Mexico, 1993.
• [Bh] L. N. Belykh, Analysis of Mathematical Models in Immunology, Nauka, Moskwa, 1988 (po rosyjsku).
• [BFl] M. Bodnar, U. Foryś, Behaviour of solutions to Marchuk’s model depending on a time delay, Internat. J. Appl. Math. Comput. Sci. 10 (2000), 97-112.
• [BF2] M. Bodnar, U. Foryś, Periodic dynamics in the model of immune system, Appl. Math. (Warsaw) 27 (2000), 113-126.
• [BF3] M. Bodnar, U. Foryś, A model of the immune system with stimulation depending on time, w: Proc. IV KKZMwBiM, Warszawa, 1998.
• [BS] F. Bofill, R. Quentallia, W. Szlenk, The Marchuk’s model in the case of vaccination. Qualitative behaviour and some applications, preprint, Politechnika Katalońska, Barcelona, 1995.
• [BSk] A. Borkowska, W. Szlenk, A mathematical model of antibody concentration decline after vaccination for hepatitis B, Polish J. Immun. 20 (1995), 117-122.
• [Co] V. Capasso, Mathematical Structures of Epidemic Systems, Springer, New York, 1996.
• [DG] O. Diekmann, S. van Giles, S. Verduyn Lunel, H. Walter, Delay Equations, Springer, New York, 1995.
• [Fśl] U. Foryś, Mathematical model of an immune system with random time of reaction, Appl Math. (Warsaw) 21 (1993), 521-536.
• [FŚ2] U. Foryś, Discrete mathematical model of an immune system, w: Mathematical Population Dynamics, 2, Wuerz Publ., 1995, 167-182.
• [FŚ3] U. Foryś, Interleukin mathematical model of an immune system, J. Biol. Sys. 3 (1995), 889-902.
• [FŚ4] U. Foryś, Global analysis of Marchuk’s model of an immune system in some special cases, w: Proc. I KKZMwBiM, Kraków, 1995.
• [FŚ5] U. Foryś, Global analysis of Marchuk’s model in a case of weak immune system, Math. Comput. Model. 25 (1997), 97-106.
• [FŚ6] U. Foryś, Global analysis of the initial value problem for a system of ODE modeling the immune system after vaccinations, Math. Comp. Model. 29 (1999), 79-85.
• [FŚ7] U. Foryś, Global analysis of Marchuk’s model in case of strong immune system, ukaże się w J. Biol. Systems.
• [FŻ1] U. Foryś, N. Żołek, A model of immune system after vaccinations, ARI 50 (1998), 180-184.
• [FZ2] U. Foryś, N. Żołek, Complementary analysis of the initial value problem for a system of o.d.e. modelling, immune system after vaccinations, Appl. Math. (Warsaw) 27 (2000), 103-111.
• [Gd] T. Gard, Introduction to Stochastic Differential Equations, Dekker, New York, 1988.
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• [HT] H. Hethcote, D. Tudor, Integral equation models for endemic infectious diseases, J. Math. Biol. 9 (1980), 37-47.
• [Ii] M. Iannelłi, The mathematical description of epidemics: some basic models and problems, w: Mathematical Aspects of Human Diseases, G. Da Prato (red.), Appl. Math. Monographs 3, C.N.R., Giardini, Pisa, 1992, 11-32.
• [Kg] Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, Boston, 1993.
• [KM] W. Kermack, A. McKendrick, A contribution to the mathematical theory of epidemics, Proc. Roy. Soc. (A) 115 (1927), 700-721.
• [KN] V. B. Kolmanovskii, V. R. Nosov, Stability of Functional Differential Equations, Academic Press, London, 1986.
• [KP] D. Kirschner, J. Panetta, Modeling immunoterapy of the tumor-immune reaction, J. Math. Biol. 37 (1998), 235-252.
• [KMn] V. A. Kuznetsov, I. A. Makalkin, M. Taylor, A. Perelson, Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis, Bull. Math. Biol. 56 (1994), 295-321.
• [Mz] S. Mackiewicz, Immunologia, PZWL, Warszawa, 1991.
• [Mkl] G. I. Marczuk, Mathematical Models in Immunology, Nauka, Moskwa, 1980 (po rosyjsku).
• [Mk2] G. I. Marczuk, Mathematical Models in Immunology, New York, Springer, 1983.
• [Mk3] G. I. Marczuk, Mathematical Modelling of Immune Response in Infectious Diseases, Kluwer, 1997.
• [MM] D. Meade, F. Milner, SIR epidemic models with direct diffusion, w: Mathematical Aspects of Human Diseases, G. Da Prato (red.), Appl. Math. Monographs 3, C.N.R., Giardini, Pisa, 1992, 79-90.
• [Mr] R. Mohler, Bilinear control structures in immunology, w: Modelling and Optimization of Complex Systems, 1979, 58-68.
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• [PW] D. Prikrilova, J. Waniewski, Some interesting results of mathematical modelling of the immune response, w: Mathematics Applied to Biology and Medicine, Wuerz Publ., 1993, 285-290.
• [Sk] W. Szlenk, Wstęp do teorii gładkich układów dynamicznych, Biblioteka Mat. 56, PWN, 1982.
• [SV] W. Szlenk, C. Vargas, Some remarks on Marchuk’s mathematical model of immune system, preprint CINVESTAV, Mexico, 1995.
• [Ui] J. Uchmański, Klasyczna ekologia matematyczna, PWN, Warszawa, 1992.

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).