Mathematical modeling and dynamical observations of HIV/AIDS transmission under the role of antiretroviral treatment

The Human Immunodeficiency Virus (HIV) attacks particular immune system cells such as Tcells (primarily CD+4T cells) and triggers lifetime severe sickness with a prolonged incubation period. This study develops and analyzes a novel mathematical model to understand the spread of the virus, using real-world data reported cases in Taiwan from 2000 to 2023. The mathematical properties of the model, such as existence, uniqueness, positivity, and boundedness, are rigorously examined to ensure reliability. Equilibrium points are determined, and their stability is analyzed to understand the long-term behavior of the disease. The fundamental reproduction number is obtained using the next generation approach. Sensitivity analysis is performed using different variables as response functions each time, employing Latin Hypercube Sampling and Partial Rank Correlation Coefficient with 200 iterations. Theoretical results are validated using numerical simulations and graphically display the impacts of different model parameters. Results indicate that reducing contact with infected individuals and accelerating disease management interventions can significantly lower the burden of infection.