Stability of Linear Delay Differential Equations Arising in Models of Living Systems

Pertsev, N. V.

doi:10.3103/s1055134420010046

Cited by 5 publications

(6 citation statements)

References 7 publications

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“…where c 1 , c 2 , c 3 are some constants, λ is a complex number. It is easy to establish, that for R 0 > 1 among the roots λ of the characteristic equation there exists a real root λ 0 > 0 [29]. This implies that for some initial data (3.47), (3.48) the solution of system (3.49)-(3.51) admits asymptotically exponential growth.…”

Section: An Example Of Numerical Simulationmentioning

confidence: 94%

“…Using the results of [29], we establish that the equilibrium (3.53) is asymptotically Lyapunov stable if det Q > 0, which is equivalent to the inequality R 0 < 1, where…”

Section: An Example Of Numerical Simulationmentioning

confidence: 99%

“…To build the model, we used publications listed in the references of [11] (articles No. 7,8,11,12,26,28,29,30), monograph [24] and articles [25], [26].…”

Section: Notation and Postulates Of The Modelmentioning

confidence: 99%

“…By analogy with Section 2.5, to plan computational experiments with the model, we use a deterministic analogue of the stochastic stage-dependent model. To construct the equations of a deterministic model and study its solutions, we will rely on the results of [10], [11], [29].…”

Section: An Example Of Numerical Simulationmentioning

confidence: 99%

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Stochastic Modeling in Immunology Based On a Stage-Dependent Framework with Non-Markov Constraints for Individual Cell and Pathogen Dynamics

Pertsev,

Loginov

2023

Math.Biol.Bioinf.

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We present a systematic approach to modelling the responses of the immune system to virus infections. Two continuous-discrete stochastic models arising in mathematical immunology are developed and computationally implemented. The variables of the models are integer random variables that denote the quantity of individuals (cells and viral particles), and sets of unique types of individuals that take into account the current state and history of stay of individuals in some stages of their development. The distribution laws of the durations of the mentioned stages are different from exponential or geometric. A probabilistic description of a one-stage stochastic model of population dynamics is presented. A stochastic model of the development of HIV-1 infection in the lymph node in the initial period after infection of a healthy person is formulated. A computational algorithm based on the Monte Carlo method is given. Each of the stochastic models is complemented by a deterministic analogue in the form of integral and delay differential equations. The results of numerical simulation are presented.

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Section: An Example Of Numerical Simulationmentioning

confidence: 94%

“…Using the results of [29], we establish that the equilibrium (3.53) is asymptotically Lyapunov stable if det Q > 0, which is equivalent to the inequality R 0 < 1, where…”

Section: An Example Of Numerical Simulationmentioning

confidence: 99%

“…To build the model, we used publications listed in the references of [11] (articles No. 7,8,11,12,26,28,29,30), monograph [24] and articles [25], [26].…”

Section: Notation and Postulates Of The Modelmentioning

confidence: 99%

Section: An Example Of Numerical Simulationmentioning

confidence: 99%

See 2 more Smart Citations

Stochastic Modeling in Immunology Based On a Stage-Dependent Framework with Non-Markov Constraints for Individual Cell and Pathogen Dynamics

Pertsev,

Loginov

2023

Math.Biol.Bioinf.

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“…Система уравнений (6.5)-(6.7) с учетом выражений (6.8)-(6.10) относится к системам специального вида (система уравнений Важевского или позитивная система с запаздыванием). Следуя [16], для анализа асимптотической устойчивости тривиального (нулевого) положения равновесия системы (6.4)-(6.7) достаточно перейти к системе (6.5)-(6.7) и использовать свойства невырожденных М-матриц [17], [18].…”

Section: устойчивость тривиального решения модели развития вич-1 инфе...unclassified

Mathematical Modeling of the Initial Period of Spread of HIV-1 Infection in the Lymphatic Node

Pertsev,

Bocharov,

Loginov

2024

Math.Biol.Bioinf.

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A mathematical model describing the initial period of spread of HIV-1 infection in a single lymphatic node of an infected individual is presented. The model variables are the quantity of viral particles, CD4+ T-lymphocytes, and antigen-presenting cells. To build the model, a high-dimensional system of differential equations with delay, supplemented initial data, is used. Some of the model equations take into account intermediate stages of development of viral particles and cells involved in the infectious process. The existence, uniqueness and non-negativity of the components of the model solutions on the semi-axis for non-negative initial data are established. Conditions for the asymptotic stability of the equilibrium state interpreted as the absence of HIV-1 infection in the lymphatic node are obtained. To solve the model numerically, a semi-implicit Euler scheme is used. The conditions for the attenuation of HIV-1 infection in the lymphatic node and the beginning of the systemic spread of infection throughout the organism of an infected individual are analyzed analytically and numerically.

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General Lagrange-hybrid functions and numerical solution of differential equations containing piecewise constant delays with bibliometric analysis

Sabermahani

Ordokhani

2021

Applied Mathematics and Computation

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Stability of Linear Delay Differential Equations Arising in Models of Living Systems

Cited by 5 publications

References 7 publications

Stochastic Modeling in Immunology Based On a Stage-Dependent Framework with Non-Markov Constraints for Individual Cell and Pathogen Dynamics

Stochastic Modeling in Immunology Based On a Stage-Dependent Framework with Non-Markov Constraints for Individual Cell and Pathogen Dynamics

Mathematical Modeling of the Initial Period of Spread of HIV-1 Infection in the Lymphatic Node

General Lagrange-hybrid functions and numerical solution of differential equations containing piecewise constant delays with bibliometric analysis

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