Human Immunodeficiency Virus (HIV) and Acquired Immunodeficiency Syndrome (AIDS) continue to be a significant public health concern despite advances in antiretroviral therapies. Understanding the transmission dynamics of HIV infection is crucial for the development of effective control strategies. In this study, a five compartment deterministic model is proposed to investigate the spread of HIV/AIDS using epidemiological data from Europe.

Structural and practical identifiability analyses are performed to evaluate the reliability of parameter estimation in the model. Structural identifiability is assessed using the SIAN (Structural Identifiability Analyser) method, which classifies parameters as globally identifiable, locally identifiable, or non-identifiable, while practical identifiability is evaluated through Monte Carlo simulations and the Average Relative Error (ARE). The basic reproduction number, R0, is computed, and sensitivity analysis is conducted to examine the impact of model parameters on disease transmission.

The parameters of this non-autonomous model are estimated based on HIV/AIDS case data from Europe for the period 2000-2023. The results indicate that the appropriate selection of observable variables significantly improves parameter identifiability. In conclusion, the proposed model provides a reliable framework for analyzing the spread of HIV/AIDS and may contribute to epidemiological forecasting and the development of effective intervention strategies.