A simulation-based analysis of a novel HIV/AIDS transmission model with awareness and treatment

The human immunodeficiency virus (HIV) continues to pose a global threat, affecting countries worldwide. Cape Verde’s HIV situation is alarming, yet the literature lacks studies exploring real HIV cases, especially in terms of awareness and treatment, using mathematical modeling with fractional derivatives. The purpose of this study is to investigate a novel mathematical model for HIV infection transmission in Cape Verde. The model incorporates a fractional Caputo derivative, crucial for predicting disease outbreaks and capturing memory and non-locality characteristics. The objective is to offer insights to effectively combat HIV infection in Cape Verde. The existence and uniqueness of solutions for the fractional HIV mathematical model are established using a fixed-point theorem and an iterative technique. A fixed-point theorem and an iterative method are used to ensure that the solutions of the fractional HIV mathematical model exist and are unique. Additionally, the positivity and boundedness of the model’s solutions are verified. The equilibrium points of the model are documented for both disease-free and endemic conditions, and the reproduction number ( \(R_0\) $R_0$ ) is determined using the next-generation approach. Latin Hyper-cube Sampling and Partial Rank Correlation Coefficient with 200 iterations are employed to analyze the sensitivity of \(R_0\) $R_0$ . The results are presented in the form of contour plots and 3-D phase portraits. Parameters are estimated using actual data on HIV cases in Cape Verde, and the model is graphically demonstrated to fit the real cases accurately. The local and global stability of the disease-free equilibrium state is demonstrated using the Routh-Hurwitz technique and the creation of a Lyapunov function with LaSalle’s principle, respectively. MATLAB software is used to execute numerical simulations with the Adams-Bashforth predictor-corrector technique. The validity of the model is confirmed by the convergence of the respective compartmental classes to their equilibrium points when considering different fractional order values. Additionally, graphical representations are provided to examine how varying the fractional order and critical model parameters influence the disease dynamics. The results of our investigation demonstrate the effectiveness of the adopted strategies in making more accurate predictions.