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

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.