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

We study stability of the trivial equilibrium of certain compartment and stage-dependent models 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 sufficient conditions for asymptotic stability of the trivial equilibrium of systems of such equations. We consider a linear model of dynamics of HIV-1 infection in the body of an infected person. We find sufficient conditions for asymptotic stability of the trivial solution of the model of dynamics of HIV-1 infection. The obtained relations between parameters of the model are interpreted as conditions for eradication of HIV-1 infection due to nonspecific factors of the immune system.