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<p>This paper primarily focuses on numerical threshold stability of a nonlinear diffusive age-structured HIV model. A semi-discrete system based on the line method is established and a threshold is introduced in the stability analysis of the resulting discrete system, which we refer to as numerical basic numerical reproduction number. A discretization technique is adopted in formulating a full-discrete numerical scheme to ensure the biological significance can be preserved without stepsize restriction. It is proved that numerical stability thresholds we proposed converge to the exact stability threshold and replicate the monotonicity and qualitative properties of the latter. Finally, the conclusions are illustrated by numerical experiments.</p>

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Threshold stability analysis of an unconditionally positivity-preserving numerical method for a nonlinear age-structured diffusive HIV model with spatial coefficients

  • 期刊论文

  • 发表日期：

    2025年1月3日

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  • Meng Zhang,
  • Xing Liu,
  • Shiyuan Yang

摘要

This paper primarily focuses on numerical threshold stability of a nonlinear diffusive age-structured HIV model. A semi-discrete system based on the line method is established and a threshold is introduced in the stability analysis of the resulting discrete system, which we refer to as numerical basic numerical reproduction number. A discretization technique is adopted in formulating a full-discrete numerical scheme to ensure the biological significance can be preserved without stepsize restriction. It is proved that numerical stability thresholds we proposed converge to the exact stability threshold and replicate the monotonicity and qualitative properties of the latter. Finally, the conclusions are illustrated by numerical experiments.