An extremal shift method for control of HIV infection dynamics

Bocharov, Gennady; Kim, A. V.; Красовский, А Н; Chereshnev, V. А.; Glushenkova, V. V.; Іванов, А. В.

doi:10.1515/rnam-2015-0002

Cited by 9 publications

(4 citation statements)

References 7 publications

(13 reference statements)

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“…The presence of bi-or multistability indicates that by perturbing a certain trajectory of the system in the phase space, the transfer of the infectious disease to a more favorable regime can be accomplished. Both classical optimal control methods (Hadjiandreou et al, 2009;Bocharov et al, 2015) and our previously proposed methods based on optimal disturbances (Nechepurenko, Khristichenko, 2019; exist as tools for constructing an appropriate control. Furthermore, there could be a case when a change in the kinetic parameters of biological and physiological processes is required to move the system into the region of bi-or multistability.…”

Section: Discussionmentioning

confidence: 99%

Bifurcation analysis of multistability and hysteresis in a model of HIV infection

Mironov,

Khristichenk,

Nechepurenko

et al. 2023

Vestn. VOGiS

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The infectious disease caused by human immunodeficiency virus type 1 (HIV-1) remains a serious threat to human health. The current approach to HIV-1 treatment is based on the use of highly active antiretroviral therapy, which has side effects and is costly. For clinical practice, it is highly important to create functional cures that can enhance immune control of viral growth and infection of target cells with a subsequent reduction in viral load and restoration of the immune status. HIV-1 control efforts with reliance on immunotherapy remain at a conceptual stage due to the complexity of a set of processes that regulate the dynamics of infection and immune response. For this reason, it is extremely important to use methods of mathematical modeling of HIV-1 infection dynamics for theoretical analysis of possibilities of reducing the viral load by affecting the immune system without the usage of antiviral therapy. The aim of our study is to examine the existence of bi-, multistability and hysteresis properties with a meaningful mathematical model of HIV-1 infection. The model describes the most important blocks of the processes of interaction between viruses and the human body, namely, the spread of infection in productively and latently infected cells, the appearance of viral mutants and the development of the T cell immune response. Furthermore, our analysis aims to study the possibilities of transferring the clinical pattern of the disease from a more severe state to a milder one. We analyze numerically the conditions for the existence of steady states of the mathematical model of HIV-1 infection for the numerical values of model parameters corresponding to phenotypically different variants of the infectious disease course. To this end, original computational methods of bifurcation analysis of mathematical models formulated with systems of ordinary differential equations and delay differential equations are used. The macrophage activation rate constant is considered as a bifurcation parameter. The regions in the model parameter space, in particular, for the rate of activation of innate immune cells (macrophages), in which the properties of bi-, multistability and hysteresis are expressed, have been identified, and the features cha rac terizing transition kinetics between stable equilibrium states have been explored. Overall, the results of bifurcation analysis of the HIV-1 infection model form a theoretical basis for the development of combination immune-based therapeutic approaches to HIV-1 treatment. In particular, the results of the study of the HIV-1 infection model for parameter sets corresponding to different phenotypes of disease dynamics (typical, long-term non-progressing and rapidly progressing courses) indicate that an effective functional treatment (cure) of HIV-1-infected patients requires the development of a personalized approach that takes into account both the properties of the HIV-1 quasispecies population and the patient’s immune status.

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Section: Discussionmentioning

confidence: 99%

Bifurcation analysis of multistability and hysteresis in a model of HIV infection

Mironov,

Khristichenk,

Nechepurenko

et al. 2023

Vestn. VOGiS

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“…For definiteness, we assume that this curve is simple, that is, it does not have multiple irreducible components. Then equality ∂Y ∂V (s, V ) = 0 (8) holds only at a finite number of points.…”

Section: 2mentioning

confidence: 99%

“…Indeed, a bistable dynamical system can be transferred to a favourable steady state using the optimal disturbance approach as outlined in [5,6,7]. In the situation of monostability, the transfer of the system away from unwanted steady state requires the implementation of control taking the system to a neighborhood of a given trajectory (e.g., feedback stabilization, extremal shift or the optimal programme (open loop) control [8]). An alternative solution could be a mixed control consisting of a parametric shift of the system to a bistable domain of the parameter space and further correction of its dynamics by optimal disturbances of the steady state.…”

mentioning

confidence: 99%

Bistability analysis of virus infection models with time delays

Nechepurenko¹,

Khristichenko²,

Grebennikov³

et al. 2020

Discrete &Amp; Continuous Dynamical Systems - S

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Mathematical models with time delays are widely used to analyze the mechanisms of the immune response to virus infections and predict various therapeutic effects. Using the lymphocytic choriomeningitis virus infection model as an example, this work describes an original computational technology for searching the bistable regimes of such models. This technology includes numerical methods for finding all possible steady states at fixed values of parameters, for tracing these states along the parameters and for analyzing their stability.2020 Mathematics Subject Classification. Primary: 97M60, 34K10, 65L07; Secondary: 37N25, 34K28, 34L16.

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“…Для бистабильной динамической системы перевод в благоприятное стационарное состояние может быть осуществлен на основе оптимальных возмущений [8,9,10]. В случае же моностабильности перевод из области нежелательного стационарного состояния предполагает применение стратегий стабилизации динамики системы по принципу обратной связи или же программного управления [11]. Альтернативой может быть комбинированное управление, состоящее из параметрического возмущения системы, переводящего ее в область бистабильности, и дальнейшая коррекция динамики путем оптимального возмущения.…”

Section: Introductionunclassified