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Viral Infection Model with Diffusion and Distributed Delay: Finite-Dimensional Global Attractor.

Alexander Rezounenko1

  • 1V.N.Karazin Kharkiv National University, Kharkiv, 61022 Ukraine.

Qualitative Theory of Dynamical Systems
|December 19, 2022
PubMed
Summary

This study analyzes a virus dynamics model with complex infection rates and delays. Researchers proved the existence of a finite-dimensional global attractor, offering insights into viral spread patterns.

Keywords:
AttractorDelay equationsEvolution equationsReaction-diffusionVirus infection model

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Area of Science:

  • Mathematical Biology
  • Virology
  • Dynamical Systems Theory

Background:

  • Understanding virus dynamics is crucial for disease control.
  • Reaction-diffusion models with logistic growth capture spatial spread and population limits.
  • Non-linear infection rates and distributed delays add complexity to biological realism.

Purpose of the Study:

  • To investigate a sophisticated virus dynamics model incorporating reaction-diffusion, logistic growth, and a general non-linear infection rate.
  • To analyze the impact of distributed delays, including state-selective delays, on viral spread.
  • To establish the existence of a finite-dimensional global attractor for the proposed dynamical system.

Main Methods:

  • Formulation of a virus dynamics model with reaction-diffusion and logistic growth.
  • Inclusion of a general non-linear functional response for infection rate.
  • Mathematical analysis within a Hilbert space framework to construct the dynamical system.
  • Proof of the existence of a finite-dimensional global attractor.

Main Results:

  • Demonstration of the existence of a global attractor for the virus dynamics model.
  • The attractor is shown to be finite-dimensional, simplifying the long-term behavior analysis.
  • The model successfully incorporates complex factors like non-linear infection and distributed delays.

Conclusions:

  • The study confirms the existence of a finite-dimensional global attractor for the complex virus dynamics model.
  • This finding provides a theoretical foundation for understanding the long-term behavior and stability of viral infections.
  • The mathematical framework developed can be applied to analyze other complex biological systems with delays and non-linearities.