Optimum control of process of application of antivirus preparations at HIV infection treatment
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 2 (2013) no. 4, pp. 94-102 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The methodological problem of application of modern mathematical and information methods for management of restoration of immune system of the person for increase in duration of his/her life is considered. Developed and numerically solved the problem of optimum control by dynamics of HIV infection on the basis of application of the principle of a maximum of Pontryagin for nonlinear systems with continuous delay and rough right part. On the basis of program realization of numerical algorithm results of modeling of dynamics of immune system are given when using various strategy of application of medicines. By transformation of basic system of the differential equations, research of influence of secondary infectious diseases on dynamics of HIV infection is conducted.
Keywords: rough nonlinear dynamic systems with delay, optimum control, mathematical models of HIV infection.
@article{VYURV_2013_2_4_a6,
     author = {I. P. Bolodurina and Yu. P. Ivanova},
     title = {Optimum control of process of application of antivirus preparations at {HIV} infection treatment},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a Vy\v{c}islitelʹna\^a matematika i informatika},
     pages = {94--102},
     year = {2013},
     volume = {2},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURV_2013_2_4_a6/}
}
TY  - JOUR
AU  - I. P. Bolodurina
AU  - Yu. P. Ivanova
TI  - Optimum control of process of application of antivirus preparations at HIV infection treatment
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika
PY  - 2013
SP  - 94
EP  - 102
VL  - 2
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VYURV_2013_2_4_a6/
LA  - ru
ID  - VYURV_2013_2_4_a6
ER  - 
%0 Journal Article
%A I. P. Bolodurina
%A Yu. P. Ivanova
%T Optimum control of process of application of antivirus preparations at HIV infection treatment
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika
%D 2013
%P 94-102
%V 2
%N 4
%U http://geodesic.mathdoc.fr/item/VYURV_2013_2_4_a6/
%G ru
%F VYURV_2013_2_4_a6
I. P. Bolodurina; Yu. P. Ivanova. Optimum control of process of application of antivirus preparations at HIV infection treatment. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 2 (2013) no. 4, pp. 94-102. http://geodesic.mathdoc.fr/item/VYURV_2013_2_4_a6/

[1] E. A. Andreeva, V. B. Kolmanovskii, L. E. Shaikhet, Management of systems with aftereffect, Nauka, Moscow, 1992, 336 pp.

[2] V. V. Velichenko, D. A. Pritykin, “Possibilities of artificial intelligence and computer technologies in development of programs for treatment of difficult immune diseases”, Fundamental and applied mathematics, 15:5 (2009), 21–42, Open systems, Moscow

[3] V. V. Velichenko, D. A. Pritykin, “Control of the medical treatment of AIDS”, Automation and Remote Control, 67:3 (2006), 437-511

[4] V. V. Velichenko, D. A. Pritykin, “Numerical methods optimum control of dynamics HIV infection”, News RAS. Theory and systems control, 2006, no. 6, 53-64

[5] V. I. Kuimov, A. N. Rapoport, “Modeling of dynamics of HIV infection”, Microsoft Technologies in the theory and practice of programming, 2010, 237–240, Nizhny Novgorod state university, Nizhny Novgorod

[6] V. V. Pokrovsk, Epidemiology and prevention of HIV infection, Medicine, Moscow, 1996, 275 pp.