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<p>This study presents a mathematical model incorporating both asymptomatic and symptomatic HIV-infected individuals to analyze the dynamics of HIV/AIDS. This expanded model offers a more comprehensive understanding of the epidemic’s spread. We calculate the basic reproduction number (R<sub>0</sub>) to quantify the virus’s transmission potential. To achieve accurate and robust simulations, we introduce the Nonstandard Finite Difference Scheme (NSFD). Compared to traditional methods like RK-4, NSFD offers improved dynamical consistency and numerical precision, leading to enhanced stability and efficiency in simulating infectious diseases like HIV/AIDS. Local and global stability analysis are performed using the Routh-Hurwitz method. The NSFD method effectively captures the dynamics of HIV propagation under various scenarios, providing valuable insights into HIV/AIDS progression. We demonstrate the superiority of the NSFD approach compared to existing methods, paving the way for further research in modeling viral infections.</p>

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Local and global stability analysis of HIV/AIDS by using a nonstandard finite difference scheme

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年2月6日

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  • Amjid Hussain Morani,
  • Maha Mohammed Saeed,
  • Muhammad Aslam,
  • Atif Mehmoud,
  • Ali Shokri,
  • Herbert Mukalazi

摘要

This study presents a mathematical model incorporating both asymptomatic and symptomatic HIV-infected individuals to analyze the dynamics of HIV/AIDS. This expanded model offers a more comprehensive understanding of the epidemic’s spread. We calculate the basic reproduction number (R0) to quantify the virus’s transmission potential. To achieve accurate and robust simulations, we introduce the Nonstandard Finite Difference Scheme (NSFD). Compared to traditional methods like RK-4, NSFD offers improved dynamical consistency and numerical precision, leading to enhanced stability and efficiency in simulating infectious diseases like HIV/AIDS. Local and global stability analysis are performed using the Routh-Hurwitz method. The NSFD method effectively captures the dynamics of HIV propagation under various scenarios, providing valuable insights into HIV/AIDS progression. We demonstrate the superiority of the NSFD approach compared to existing methods, paving the way for further research in modeling viral infections.