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.
@article{bwmeta1.element.bwnjournal-article-amcv13i3p407bwm, author = {Szyma\'nska, Zuzanna}, title = {Analysis of immunotherapy models in the context of cancer dynamics}, journal = {International Journal of Applied Mathematics and Computer Science}, volume = {13}, year = {2003}, pages = {407-418}, zbl = {1035.92023}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv13i3p407bwm} }
Szymańska, Zuzanna. Analysis of immunotherapy models in the context of cancer dynamics. International Journal of Applied Mathematics and Computer Science, Tome 13 (2003) pp. 407-418. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv13i3p407bwm/
[000] Chen Ch.-H. and Wu T.-C. (1998): Experimental vaccine strategies for cancer immunotherapy. - J. Biomed. Sci., Vol. 5, No. 4, pp. 231-252.
[001] Connor M. and Ferguson-Smith M., (1997) Essential Medical Genetics. - Oxford: Blachwell Science.
[002] Foryś U. (2002): Marchuk's model of immune system dynamics with application to tumour growth. - J. Theoret. Med., Vol. 4, No. 1, pp. 85-93. | Zbl 1059.92031
[003] Greenspan H.P. (1972): Models for the growth of a solid tumor by diffusion. - Stud. Appl. Math., Vol. 51, No. 4, pp. 317-340. | Zbl 0257.92001
[004] Hartman P.H. (1964): Ordinary Differential Equations. - New York: Wiley. | Zbl 0125.32102
[005] Jakóbisiak M. (Ed.) (1995): Immunology. - Warsaw: Polish Scientific Publishers, (in Polish).
[006] Kirschner D. and Panetta J., (1998): Modeling immunotherapy ofthe tumor - immune interaction. - J. Math. Biol., Vol. 37, No. 3, pp. 235-252. | Zbl 0902.92012
[007] Kuby J. (1997): Immunology. - New York: Freeman Co.
[008] 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.
[009] Michałkiewicz J. (2003): Personal communication. - Department of Clinical Immunology, Children Memorial Health Institute, Warsaw.
[010] Villasana M. (2001): A Delay Differential Equation Model for TumorGrowth. - Ph.D. thesis, Dept. Mathematics, Claremont University, USA.
[011] Terry W. and Yamamura Y. (Ed.) (1979): Immunobiology and Immunotherapyof Cancer. - North-Holland: Elsevier.
[012] Traczyk W. (1997): Human phisiology. - Warsaw: PZWL, (in Polish).
[013] Turowicz A. (1967): Geometry of the zeros of the polynomials. - Warsaw: Scientific Publishers, (in Polish).