Bifurcation analysis of multistability and hysteresis in a model of HIV infection
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 import...
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Siberian Branch of the Russian Academy of Sciences, Federal Research Center Institute of Cytology and Genetics, The Vavilov Society of Geneticists and Breeders
2023-12-01
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| Series: | Вавиловский журнал генетики и селекции |
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| Online Access: | https://vavilov.elpub.ru/jour/article/view/3975 |
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| author | I. V. Mironov M. Yu. Khristichenk Yu. M. Nechepurenko D. S. Grebennikov G. A. Bocharov |
| author_facet | I. V. Mironov M. Yu. Khristichenk Yu. M. Nechepurenko D. S. Grebennikov G. A. Bocharov |
| author_sort | I. V. Mironov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-85c9130f2f634f159341b3587ff59cf1 |
| institution | Kabale University |
| issn | 2500-3259 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Siberian Branch of the Russian Academy of Sciences, Federal Research Center Institute of Cytology and Genetics, The Vavilov Society of Geneticists and Breeders |
| record_format | Article |
| series | Вавиловский журнал генетики и селекции |
| spelling | doaj-art-85c9130f2f634f159341b3587ff59cf12025-02-01T09:58:12ZengSiberian Branch of the Russian Academy of Sciences, Federal Research Center Institute of Cytology and Genetics, The Vavilov Society of Geneticists and BreedersВавиловский журнал генетики и селекции2500-32592023-12-0127775576710.18699/VJGB-23-881403Bifurcation analysis of multistability and hysteresis in a model of HIV infectionI. V. Mironov0M. Yu. Khristichenk1Yu. M. Nechepurenko2D. S. Grebennikov3G. A. Bocharov4Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences; Sechenov First Moscow State Medical University of the Ministry of Health of the Russian FederationKeldysh Institute of Applied Mathematics of the Russian Academy of Sciences; Marchuk Institute of Numerical Mathematics of the Russian Academy of SciencesKeldysh Institute of Applied Mathematics of the Russian Academy of Sciences; Marchuk Institute of Numerical Mathematics of the Russian Academy of SciencesSechenov First Moscow State Medical University of the Ministry of Health of the Russian Federation; Marchuk Institute of Numerical Mathematics of the Russian Academy of SciencesSechenov First Moscow State Medical University of the Ministry of Health of the Russian Federation; Marchuk Institute of Numerical Mathematics of the Russian Academy of SciencesThe 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.https://vavilov.elpub.ru/jour/article/view/3975mathematical modelhiv infectionordinary differential equationsbifurcation analysisstationary solutionsbistabilitymultistabilityhysteresisoptimal control |
| spellingShingle | I. V. Mironov M. Yu. Khristichenk Yu. M. Nechepurenko D. S. Grebennikov G. A. Bocharov Bifurcation analysis of multistability and hysteresis in a model of HIV infection Вавиловский журнал генетики и селекции mathematical model hiv infection ordinary differential equations bifurcation analysis stationary solutions bistability multistability hysteresis optimal control |
| title | Bifurcation analysis of multistability and hysteresis in a model of HIV infection |
| title_full | Bifurcation analysis of multistability and hysteresis in a model of HIV infection |
| title_fullStr | Bifurcation analysis of multistability and hysteresis in a model of HIV infection |
| title_full_unstemmed | Bifurcation analysis of multistability and hysteresis in a model of HIV infection |
| title_short | Bifurcation analysis of multistability and hysteresis in a model of HIV infection |
| title_sort | bifurcation analysis of multistability and hysteresis in a model of hiv infection |
| topic | mathematical model hiv infection ordinary differential equations bifurcation analysis stationary solutions bistability multistability hysteresis optimal control |
| url | https://vavilov.elpub.ru/jour/article/view/3975 |
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