论文信息 - ANALYSIS OF IMMUNOTHERAPY MODELS IN THE CONTEXT OF CANCER DYNAMICS

ANALYSIS OF IMMUNOTHERAPY MODELS IN THE CONTEXT OF CANCER DYNAMICS

A basic mathematical model of the immune response when cancer cells are recognized is proposed. The model consists of six ordinary differential equations. It is extended by taking into account two types of immunotherapy: active immunotherapy and adoptive immunotherapy. An analysis of the corresponding models is made to answer the question which of the presented methods of immunotherapy is better. The analysis is completed by numerical simulations which show that the method of adoptive immunotherapy seems better for the patient at least in some cases.

Zuzanna Szyma

[1] Malcolm A. Ferguson-Smith,et al. Essential Medical Genetics , 1997, Annals of Internal Medicine.

[2] W. Terry,et al. Immunobiology and immunotherapy of cancer , 1979 .

[3] Urszula Foryś,et al. Marchuk's Model of Immune System Dynamics with Application to Tumour Growth , 2002 .

[4] H. Greenspan. Models for the Growth of a Solid Tumor by Diffusion , 1972 .

[5] P. Hartman. Ordinary Differential Equations , 1965 .

[6] D. Kirschner,et al. Modeling immunotherapy of the tumor – immune interaction , 1998, Journal of mathematical biology.

[7] Ami Radunskaya,et al. A delay differential equation model for tumor growth , 2003, Journal of mathematical biology.

[8] U. an der Heiden,et al. A basic mathematical model of the immune response. , 1995, Chaos.