TURK 2025

The main aim of this paper is to investigate a nonlinear HIV/AIDS epidemic model. The effect of sexual transmission is involved which later results in AIDS. The fixed points of the model are obtained and their local and global stability analysis is carried out. The existence and uniqueness of qualitative results are presented. We develop a numerical scheme for the proposed HIV/AIDS epidemic system. The developed method is utilized to demonstrate the efficiency of the model for numerical results. This study plays a key role in controlling infectious factors in epidemic problems. This research provides a robust foundation for understanding HIV/AIDS system dynamics, with implications for public health policies, healthcare resource allocation, and HIV therapy advancements. This study could lead to better patient outcomes and the creation of more potent HIV treatments by deepening our understanding of the intricate dynamics of HIV/AIDS.