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Revisiting the classical target cell limited dynamical within-host HIV model - Basic mathematical properties and

Benjamin Wacker1

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|January 14, 2025
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Summary

This study analyzes the CD4+ T cell and HIV dynamics model. Mathematical analysis confirms the stability of virus-free and plateau-phase equilibria, supported by numerical simulations.

Keywords:
dynamical systemequilibriaexistencenon-negativitystabilityuniquenesswithin-host HIV model

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Area of Science:

  • Mathematical Biology
  • Virology
  • Immunology

Background:

  • The human immunodeficiency virus (HIV) primarily targets CD4+ T cells.
  • Understanding within-host viral dynamics is crucial for HIV infection management.

Purpose of the Study:

  • To mathematically analyze a simplified within-host HIV model focusing on CD4+ T cell and virus interactions.
  • To investigate the stability of key disease states within the model.

Main Methods:

  • Analytical investigation of a system of differential equations.
  • Proof of non-negativity, boundedness, global existence, and uniqueness of solutions.
  • Application of the Routh-Hurwitz criterion for stability analysis.
  • Numerical simulations using Runge-Kutta methods.

Main Results:

  • Established theoretical properties of the dynamical system, including solution behavior.
  • Demonstrated local asymptotic stability for both the virus-free and plateau-phase equilibria under specific conditions.
  • Validated analytical findings through numerical experiments.

Conclusions:

  • The mathematical model provides a stable framework for understanding HIV dynamics.
  • Theoretical results on equilibrium stability are supported by numerical evidence.
  • The study suggests avenues for extending the model to more complex HIV infection scenarios.