Bistability analysis of virus infection models with time delays

Nechepurenko, Yu. M.; Khristichenko, M. Yu.; Grebennikov, Dmitry; Bocharov, Gennady

doi:10.3934/dcdss.2020166

Cited by 8 publications

(3 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It provides the possibility of switching between different virus load states. Computational models are helpful in this context as they can identify the required parameter values for the multiple steady states ( 28 ). For example, a 2-times reduction of the net virus growth rate β is the necessary condition for the existence of the low virus load state in persistent LCMV infection ( Figure 1B ).…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Functional cure of a chronic virus infection by shifting the virus - host equilibrium state

Bocharov

Grebennikov²,

Rica³

et al. 2022

Front. Immunol.

Self Cite

View full text Add to dashboard Cite

The clinical handling of chronic virus infections remains a challenge. Here we describe recent progress in the understanding of virus - host interaction dynamics. Based on the systems biology concept of multi-stability and the prediction of multiplicative cooperativity between virus-specific cytotoxic T cells and neutralising antibodies, we argue for the requirements to engage multiple immune system components for functional cure strategies. Our arguments are derived from LCMV model system studies and are translated to HIV-1 infection.

show abstract

Section: Discussionmentioning

confidence: 99%

“…(B) Mathematical model predictions of multiple virus equilibrium states (I to IV) in LCMV infections of mice as a function of the net virus growth rate β. Data are from ( 28 ). The four virus equilibrium states differ in their values of the virus load from the highest (state I) to the lowest (state IV).…”

Section: Introductionmentioning

confidence: 99%

Functional cure of a chronic virus infection by shifting the virus - host equilibrium state

Bocharov

Grebennikov²,

Rica³

et al. 2022

Front. Immunol.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Symbolic computation methods (Geddes et al, 1992) implemented in the NSolve procedure of Mathematica were used to find steady states for given parameter values. To trace the solutions by varying parameters (i. e., to investigate the dependence of steady states of the system (1-11) on the parameters), we used the original algorithm proposed in (Nechepurenko et al, 2020). The study of asymptotic stability of a given steady state was reduced to the computation of eigenvalues of the system linearized with respect to this steady state and checking that all the found eigenvalues lie strictly in the left half-plane.…”

Section: Methodsmentioning

confidence: 99%

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

Mironov,

Khristichenk,

Nechepurenko

et al. 2023

Vestn. VOGiS

View full text Add to dashboard Cite

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.

show abstract

Optimal disturbances for periodic solutions of time-delay differential equations

Khristichenko

Nechepurenko

2022

Russian Journal of Numerical Analysis and Mathematical Modelling

View full text Add to dashboard Cite

A concept of optimal disturbances of periodic solutions for a system of time-delay differential equations is defined. An algorithm for computing the optimal disturbances is proposed and justified. This algorithm is tested on the known system of four nonlinear time-delay differential equations modelling the dynamics of the experimental infection caused by the lymphocytic choriomeningitis virus. The results of numerical experiments are discussed.

show abstract

Bistability analysis of virus infection models with time delays

Cited by 8 publications

References 21 publications

Functional cure of a chronic virus infection by shifting the virus - host equilibrium state

Functional cure of a chronic virus infection by shifting the virus - host equilibrium state

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

Optimal disturbances for periodic solutions of time-delay differential equations

Contact Info

Product

Resources

About