of the Urals

Russian Journal of Agricultural Research

The publication is registered by the Ministry of the Russian Federation
for Affairs of the Press, Television and Radio Broadcasting and Mass Communication Media.
Registration certificate: PI number 77-12831 on May 31, 2002
Subscription index in catalog «Russian Press» - 16356
ISSN 1997 - 4868 (Print)

The Journal is included in the list of the leading peer-reviewed scientific journals and publications, which should be published by the main results of theses for the degree of doctor and Ph.D.
The Journal is included in the Russian Science Citation Index.
Journal is included in the list of VAK (from 25.09.2017), No. 291

ISSN 2307-0005 (Online)
Key title: Agrarnyj vestnik Urala (Online)
Abbreviated key title: Agrar. vestn. Urala (Online)

Аграрный вестник Урала № 04 (171) 2018

Биология и биотехнологии

Иванов А. В.

Ким А. В. доктор физико-математических наук, руководитель группы функционально-дифференциальных уравнений Институт математики и механики Уральского отделения Российской академии наук

УДК:51-76; 517.977.8; 519.837


We consider problem of control of conflict-controlled HIV processformalized in the form of an antagonistic differential game between twopersons. The first player is responsible for the formation of the optimal structuredtreatment interruption (STI) scenario and aims, under all possible actions ofthe second player, to lead the HIV process from the viral dominance state tothe immune dominance state, while delivering the minimum value of cost function.The second player pursues opposite goals. It is shown that the problem offinding the optimal STI scenario reduces to solving large-scale discretecombinatorial optimization problem. A method based on suboptimal STI scenarios,proposed earlier for unconflicted HIV-model control problem, is applied fordimensionality reduction of the combinatorial optimization problem, Ageneralization of this method to the case of conflict-control HIV models iscarried out. The problem of constructing a suboptimal game STI scenario isformalized in the presence of a factor of insufficient adherence of the patientto drug therapy. It is numerically shown that the non-linear HIV-modelCallaway-Perelson, described in the form of a system of ordinary differentialequations, is sensitive to singledisturbances of the suboptimal STI scenario. For the model we presented the results of numerical construction of asuboptimal game STI scenario that is resistant to single disturbances of drug regimen. The results of numerical simulation showed the stabilityof the constructed suboptimal game scenario to single skipping of drugs. Thedeveloped method can be applied to the development and research of interruptibleantiretroviral therapy schemes that are resistant to such uncertainties as theresistance of the virus to antiretroviral drugs, insufficient adherence of thepatient to therapy, individual features of the pharmacokinetics andpharmacodynamics of antiretroviral drugs.


HIV infection, interrupted therapy, conflict-control HIV-model, game control, suboptimal scenario.


1. Introduction to the problems of modeling and control of HIV infection dynamic / V. A. Chereshnev et al. M.; Izhevsk : Institute of computer research, 2016. 230 p. (In Russian)

2. Attarian A., Tran H. An Optimal Control Approach to Structured Treatment Interruptions for HIV Patients: A Personalized Medicine Perspective // Applied Mathematics. 2017. Vol. 8. No. 7. P. 934–955.

3. Adams B. M., Banks H. T., Kwon H. D., Tran H. T. Dynamic multidrug therapies for HIV: Optimal and STI control approaches // Math. Biosci. Eng. 2004. Vol. 1. No. 2. P. 223–241.

4. Meza M. E. M., Bhaya A. Virus dynamics model subjected to a hybrid on-off control // J. Biol. Systems. 2010. Vol. 18. No. 2. P. 339–356.

5. Jang T. S., Kim J., Kwon H. D., Lee J. Hybrid on-off controls for an HIV model based on a linear control problem // J. Korean Math. Soc. 2015. Vol. 52. No. 3. P. 469–487.

6. Krasovskii N. N., Subbotin A. I. Positional differential games. M. : Nauka, 1976. 456 p. (In Russian)

7. Wu J., Zhang M. A Game Theoretical Approach to Optimal Control of Dual Drug Delivery for HIV Infection Treatment // IEEE Trans. Syst. Man, and Cybern. B Cybern. 2010. Vol. 40. No. 3. P. 694–702.

8. Buratto A., Cesaretto R., Zamarchi R. HIV vs. the Immune System: A Differential Game // Mathematics. 2015. Vol. 3. No 4. P. 1139–1170.

9. Jang T., Kwon H. D., Lee J. Free terminal time optimal control problem of an HIV model based on a conjugate gradient method // Bull. Math. Biol. 2011. Vol. 73. No. 10. P. 2408–2429.

10. An extremal shift method for control of HIV infection dynamics / G. Bocharov, A. V. Kim, A. Krasovskii, V. A. Chereshnev, V. Glushenkova, A. Ivanov // Russian Journal of Numerical Analysis and Mathematical Modelling. 2015. Vol. 30. No 1. P. 11–25.

Download article as PDF:

3.pdf (735 KB)

Our database contains 2917 authors

We have published 2740 articles in 133 issues.