Analysis of immunotherapy models in the context of cancer dynamics

Zuzanna Szymańska

International Journal of Applied Mathematics and Computer Science (2003)

  • Volume: 13, Issue: 3, page 407-418
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Szymańska, Zuzanna. "Analysis of immunotherapy models in the context of cancer dynamics." International Journal of Applied Mathematics and Computer Science 13.3 (2003): 407-418. <http://eudml.org/doc/207654>.

@article{Szymańska2003,
abstract = {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.},
author = {Szymańska, Zuzanna},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {vaccination; cancer; immune system; dynamic systems},
language = {eng},
number = {3},
pages = {407-418},
title = {Analysis of immunotherapy models in the context of cancer dynamics},
url = {http://eudml.org/doc/207654},
volume = {13},
year = {2003},
}

TY - JOUR
AU - Szymańska, Zuzanna
TI - Analysis of immunotherapy models in the context of cancer dynamics
JO - International Journal of Applied Mathematics and Computer Science
PY - 2003
VL - 13
IS - 3
SP - 407
EP - 418
AB - 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.
LA - eng
KW - vaccination; cancer; immune system; dynamic systems
UR - http://eudml.org/doc/207654
ER -

References

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  8. Kuby J. (1997): Immunology. - New York: Freeman Co. 
  9. Mayer H., Zaenker K.S. and an der Heiden U. (1995): A basic mathematical model of the immune response. - Chaos, Vol. 5, No. 1, pp. 155-161. 
  10. Michałkiewicz J. (2003): Personal communication. - Department of Clinical Immunology, Children Memorial Health Institute, Warsaw. 
  11. Villasana M. (2001): A Delay Differential Equation Model for TumorGrowth. - Ph.D. thesis, Dept. Mathematics, Claremont University, USA. 
  12. Terry W. and Yamamura Y. (Ed.) (1979): Immunobiology and Immunotherapyof Cancer. - North-Holland: Elsevier. 
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  14. Turowicz A. (1967): Geometry of the zeros of the polynomials. - Warsaw: Scientific Publishers, (in Polish). 

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