Stability of solutions to linear systems of population dynamics differential equations with variable delay

The problem of stability of the trivial equilibrium position of some compartment and stage-dependent models of population dynamics based on linear differential equations with variable delay is investigated. Sufficient conditions for the asymptotic stability of the trivial equilibrium position of the studied systems of differential equations based on the method of monotone operators and the properties of M-matrices are established. A linear model of the dynamics of HIV-1 infection in the body of an infected person is considered. Sufficient conditions for asymptotic stability of a trivial solution to the HIV-1 infection dynamics model have been established. The found ratios for the model parameters are interpreted as conditions for the eradication of HIV-1 infection due to non-specific factors of the immune system.