Modelling Tumour-Immunity Interactions With Different Stimulation Functions

• Autorzy: Zhivkov P. , Waniewski J.
• Języki publikacji: EN

Abstrakty

EN

Tumour immunotherapy is aimed at the stimulation of the otherwise inactive immune system to remove, or at least to restrict, the growth of the original tumour and its metastases. The tumour-immune system interactions involve the stimulation of the immune response by tumour antigens, but also the tumour induced death of lymphocytes. A system of two non-linear ordinary differential equations was used to describe the dynamic process of interaction between the immune system and the tumour. Three different types of stimulation functions were considered: (a) Lotka-Volterra interactions, (b) switching functions dependent on the tumour size in the Michaelis-Menten form, and (c) Michaelis-Menten switching functions dependent on the ratio of the tumour size to the immune capacity. The linear analysis of equilibrium points yielded several different types of asymptotic behaviour of the system: unrestricted tumour growth, elimination of tumour or stabilization of the tumour size if the initial tumour size is relatively small, otherwise unrestricted tumour growth, global stabilization of the tumour size, and global elimination of the tumour. Models with switching functions dependent on the tumour size and the tumour to the immune capacity ratio exhibited qualitatively similar asymptotic behaviour.

Słowa kluczowe

EN

ordinary differential equations; critical points; stability analysis; immunotherapy

PL

równanie różniczkowe zwyczajne; punkt krytyczny; analiza stabilności

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2003
• Tom: Vol. 13, no 3
• Strony: 307--315
• Opis fizyczny: Bibliogr. 12 poz., wykr.

Twórcy

autor

Zhivkov P.

• Institute of Applied Mathematics and Mechanics, Warsaw University, ul. Banacha 2, 02–097 Warsaw, Poland

autor

Waniewski J.

• Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, Warsaw, Poland; Interdisciplinary Center for Mathematical and Computer Modelling Warsaw University, Warsaw, Poland

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