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

Area of Science:

• Mathematical modeling
• Epidemiology
• Computational biology

Background:

• HIV/AIDS remains a significant global health challenge.
• Accurate modeling is crucial for understanding disease dynamics and control.
• Existing models may not fully capture the complexities of HIV transmission.

Purpose of the Study:

• To develop an enhanced mathematical model for HIV/AIDS dynamics.
• To incorporate both asymptomatic and symptomatic individuals for a comprehensive analysis.
• To evaluate the efficacy of the Nonstandard Finite Difference Scheme (NSFD) in simulating HIV/AIDS progression.

Main Methods:

• Development of a compartmental mathematical model for HIV/AIDS.
• Calculation of the basic reproduction number (R0) to assess transmission potential.
• Implementation and validation of the Nonstandard Finite Difference Scheme (NSFD) for numerical simulations.
• Application of Routh-Hurwitz stability criteria for local and global analysis.

Main Results:

• The NSFD method demonstrates improved dynamical consistency and numerical precision over traditional methods like RK-4.
• The model effectively captures HIV propagation dynamics under various scenarios.
• The study quantifies the transmission potential using the basic reproduction number (R0).
• NSFD provides enhanced stability and efficiency for infectious disease simulations.

Conclusions:

• The NSFD approach offers a superior and more robust method for modeling infectious diseases like HIV/AIDS.
• The enhanced model provides valuable insights into HIV/AIDS progression and epidemic dynamics.
• This work paves the way for advanced research in mathematical modeling of viral infections.
• NSFD enhances the accuracy and efficiency of simulations for public health interventions.