# Viral infection model with diffusion and state-dependent delay: stability of classical solutions

## TL;DR

This paper analyzes the stability of classical solutions in a reaction-diffusion virus model incorporating intracellular state-dependent delay and nonlinear infection rates, using Lyapunov functions to study interior infection equilibria relevant to chronic diseases.

## Contribution

It introduces a reaction-diffusion virus model with state-dependent delay and nonlinear infection response, providing stability analysis for solutions with realistic initial conditions.

## Key findings

- Lyapunov functions establish stability of infection equilibria.
- Model accommodates discontinuous parameter changes like drug administration.
- Provides insights into chronic disease dynamics.

## Abstract

A class of reaction-diffusion virus dynamics models with intracellular state-dependent delay and a general non-linear infection rate functional response is investigated. We are interested in classical solutions with Lipschitz in-time initial functions which are adequate to the discontinuous change of parameters due to, for example, drug administration. The Lyapunov functions technique is used to analyse stability of interior infection equilibria which describe the cases of a chronic disease.