Geodesic
Optimal control of the dynamics of interaction between the human immune system and the infectious diseases
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 8 (2009), pp. 138-153 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

To evaluate and forecast the dynamics of populations of immunocompetent cells a controlled mathematical model presented by discontinuous system of nonlinear differential equations with constant delay in the phase variable is constructed. To construct the optimal control the selection of quality, relevant health criterion of the average speed of the damage of the body, reflecting the goal of management is carried out. Based on the obtained for the construction of optimal control with discontinuous right-hand side and the delay of necessary optimality conditions algorithmic and software tools with the help of which we construct the optimal treatment of infectious diseases are developed and advice on choosing the best of them is given.
Keywords: immunity, mathematical model, optimal control, оptimal treatment program.
Mots-clés : immune response 
@article{VSGU_2009_8_a13,
     author = {I. P. Bolodurina and Yu. P. Lugovskova},
     title = {Optimal control of the dynamics of interaction between the human immune system and the infectious diseases},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {138--153},
     year = {2009},
     number = {8},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2009_8_a13/}
}
TY  - JOUR
AU  - I. P. Bolodurina
AU  - Yu. P. Lugovskova
TI  - Optimal control of the dynamics of interaction between the human immune system and the infectious diseases
JO  - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
PY  - 2009
SP  - 138
EP  - 153
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/VSGU_2009_8_a13/
LA  - ru
ID  - VSGU_2009_8_a13
ER  - 
%0 Journal Article
%A I. P. Bolodurina
%A Yu. P. Lugovskova
%T Optimal control of the dynamics of interaction between the human immune system and the infectious diseases
%J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
%D 2009
%P 138-153
%N 8
%U http://geodesic.mathdoc.fr/item/VSGU_2009_8_a13/
%G ru
%F VSGU_2009_8_a13
I. P. Bolodurina; Yu. P. Lugovskova. Optimal control of the dynamics of interaction between the human immune system and the infectious diseases. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 8 (2009), pp. 138-153. http://geodesic.mathdoc.fr/item/VSGU_2009_8_a13/

[1] Belykh L. N., Marchuk G. I., Analiz matematicheskikh modelei v immunologii, Nauka, M., 1988, 192 pp. | MR | Zbl

[2] Dasgupt D., Iskusstvennye immunnye sistemy i ikh primenenie, FIZMATLIT, M., 2006, 344 pp.

[3] Bolodurina I. P., Lugovskova Yu. P., “Modelirovanie optimalnykh strategii lecheniya s uchetom energeticheskikh zatrat protivoinfektsionnoi zaschity”, Matematicheskaya teoriya sistem, materialy mezhdunarodnoi konferentsii, ISA RAN, M., 2009, 142–149

[4] Marchuk G. I., Matematicheskie modeli v immunologii, Nauka, M., 1980, 264 pp. | MR

[5] Pogozhev I. B., Marchuk G. I., Primenenie matematicheskikh modelei zabolevanii v klinicheskoi praktike, Nauka, M., 1988, 192 pp. | MR | Zbl