Estimates of solutions in a model of antiviral immune response

TL;DR

This paper analyzes a delay differential equation model of antiviral immune response, establishing stability conditions and estimates for the rate of stabilization of a healthy state using Lyapunov-Krasovskii functionals.

Contribution

It provides new stability estimates and attraction set bounds for a delay differential system modeling immune response, extending previous work by G.I. Marchuk.

Findings

Stability conditions for the healthy immune state are derived.

Estimates of the attraction set for the stationary solution are provided.

Rates of stabilization at infinity are characterized.

Abstract

We consider a model of antiviral immune response proposed in the works of G.I. Marchuk. The model is described by a system of delay differential equations. The asymptotic stability of a stationary solution to the system corresponding to a completely healthy organism is studied. Estimates of the attraction set of the given stationary solution are obtained and estimates of solutions characterizing the stabilization rate at infinity are established. The results are obtained using the Lyapunov-Krasovskii functional.