Structure preserving numerical analysis of HIV/AIDS epidemic model

Human immunodeficiency virus (HIV) remains a major global health concern. This study presents a mathematical model using ordinary differential equations with a saturated incidence rate to analyse HIV transmission dynamics. The basic reproduction number R0 is derived, indicating disease-free equilibrium stability when R0 < 1, and endemic stability when R0 >1. Unlike conventional models, we employ structure-preserving numerical schemes to ensure biologically consistent solutions and unconditional stability. Two numerical approaches are developed, the standard finite difference (SFD) and non-standard finite difference (NSFD) methods. While SFD shows conditional convergence, the NSFD scheme provides unconditionally stable and positive solutions, even with large time steps. Numerical experiments confirm the accuracy and practicality of the proposed NSFD approach. This model and method can be extended to other infectious diseases, such as hepatitis and whooping cough, offering a robust tool for long-term epidemiological analysis and control strategy assessment.