Geodesic
Numerical modelling of the reaction of the immune system to the tumor based on the revised model of Resigno and De Lisi
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 2, pp. 103-109

Voir la notice de l'article provenant de la source Math-Net.Ru

The article is devoted to the modelling of the immune response for the presence of cancer at initial stage. At this stage the key role in the development of disease is given to the immune system. It is the immunological insufficiency that is a major cause of high incidence of malignant neoplasms. The article describes the mathematical model of the immune response to the tumor. The presented model is based on the mathematical model of Resigno and De Lisi. In the created model, unlike the classical one, we take into account the fact that the presence of cancer overwhelmingly affects the immune system, and assumes the possibility of introducing of outside lymphocytes for immune response stimulation. This article provides an example of numerical prediction of tumor development, based on the constructed model. In addition the paper describes an algorithm for determining of the optimal level of input lymphocytes. The algorithm is based on the analysis of singular points of the system and numerical simulation.
Keywords: mathematical model; immune response; tumor. 
@article{VYURU_2016_9_2_a8,
     author = {N. I. Eremeeva},
     title = {Numerical modelling of the reaction of the immune system to the tumor based on the revised model of {Resigno} and {De} {Lisi}},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {103--109},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2016_9_2_a8/}
}
TY  - JOUR
AU  - N. I. Eremeeva
TI  - Numerical modelling of the reaction of the immune system to the tumor based on the revised model of Resigno and De Lisi
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
PY  - 2016
SP  - 103
EP  - 109
VL  - 9
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VYURU_2016_9_2_a8/
LA  - ru
ID  - VYURU_2016_9_2_a8
ER  - 
%0 Journal Article
%A N. I. Eremeeva
%T Numerical modelling of the reaction of the immune system to the tumor based on the revised model of Resigno and De Lisi
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
%D 2016
%P 103-109
%V 9
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VYURU_2016_9_2_a8/
%G ru
%F VYURU_2016_9_2_a8
N. I. Eremeeva. Numerical modelling of the reaction of the immune system to the tumor based on the revised model of Resigno and De Lisi. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 2, pp. 103-109. http://geodesic.mathdoc.fr/item/VYURU_2016_9_2_a8/