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Abstract <p> We study stability of the trivial equilibrium of certain compartment and stage-dependentmodels of population dynamics that are based on linear differential equations with variable delay.We use the method of monotone operators and properties of M-matrices and establish sufficientconditions for asymptotic stability of the trivial equilibrium of systems of such equations. Weconsider a linear model of dynamics of HIV-1 infection in the body of an infected person. We findsufficient conditions for asymptotic stability of the trivial solution of the model of dynamics ofHIV-1 infection. The obtained relations between parameters of the model are interpreted asconditions for eradication of HIV-1 infection due to nonspecific factors of the immune system.</p>

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Stability of Solutions of Linear Systems of Differential Equations of Population Dynamics with Variable Delay

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • N. V. Pertsev

摘要

Abstract

We study stability of the trivial equilibrium of certain compartment and stage-dependentmodels of population dynamics that are based on linear differential equations with variable delay.We use the method of monotone operators and properties of M-matrices and establish sufficientconditions for asymptotic stability of the trivial equilibrium of systems of such equations. Weconsider a linear model of dynamics of HIV-1 infection in the body of an infected person. We findsufficient conditions for asymptotic stability of the trivial solution of the model of dynamics ofHIV-1 infection. The obtained relations between parameters of the model are interpreted asconditions for eradication of HIV-1 infection due to nonspecific factors of the immune system.