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<p>This paper develops and analyzes a reaction-diffusion epidemic model to study the transmission dynamics of Human Immunodeficiency Virus (HIV). The model incorporates interactions among five distinct demographic groups to better capture the heterogeneity of disease spread. The primary objective is to investigate how spatial diffusion and treatment affect the long-term behavior of HIV transmission. Using the next-generation matrix approach, we derive the basic reproduction number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal{R}_0\)</EquationSource> </InlineEquation> and examine the stability of both the disease-free and endemic equilibria. Existence of traveling wave solutions is analyzed within the framework of monotone dynamical systems. Numerical simulations are carried out using the Crank-Nicolson operator splitting method in both diffusive and non-diffusive settings. The results illustrate that diffusion plays a significant role in shaping spatial transmission patterns, and that effective treatment strategies can reduce <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal{R}_0\)</EquationSource> </InlineEquation> below unity, leading to eradication. These findings validate the theoretical analysis and highlight the importance of incorporating spatial effects when designing HIV control strategies.</p>

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Quantitative assessment of HIV transmission dynamics with spatial diffusion: parameter estimation

  • 期刊论文

  • 发表日期：

    2026年1月3日

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  • Yuxin Wang,
  • Qi Liu,
  • Jinyu Xia,
  • Mengmeng Bao,
  • Anwarud Din

摘要

This paper develops and analyzes a reaction-diffusion epidemic model to study the transmission dynamics of Human Immunodeficiency Virus (HIV). The model incorporates interactions among five distinct demographic groups to better capture the heterogeneity of disease spread. The primary objective is to investigate how spatial diffusion and treatment affect the long-term behavior of HIV transmission. Using the next-generation matrix approach, we derive the basic reproduction number \(\mathcal{R}_0\) and examine the stability of both the disease-free and endemic equilibria. Existence of traveling wave solutions is analyzed within the framework of monotone dynamical systems. Numerical simulations are carried out using the Crank-Nicolson operator splitting method in both diffusive and non-diffusive settings. The results illustrate that diffusion plays a significant role in shaping spatial transmission patterns, and that effective treatment strategies can reduce \(\mathcal{R}_0\) below unity, leading to eradication. These findings validate the theoretical analysis and highlight the importance of incorporating spatial effects when designing HIV control strategies.