@article{Yang2025, 
author = {Mi Yang and Da-peng Gao and Shi-qiang Feng and Jin-dong Li},
title = {Dynamic analysis of a fractional-order HIV/AIDS model with generalized nonlinear incidence rate},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {10},
pages = {25049-25084},
keywords = {caputo fractional derivative, reproduction number, local stability, global stability},
url = {https://www.sciopen.com/article/10.3934/math.20251110},
doi = {10.3934/math.20251110},
abstract = {This paper investigates a fractional-order human immunodeficiency virus (HIV)/acquired immune deficiency syndrome (AIDS) model with generalized nonlinear incidence rates    f  (  S  ,  I  ) and    g  (  S  ,  E  ). First, the existence, uniqueness, non-negativity, and boundedness of the model solutions are proven, and the basic reproduction number        R    0    α   is derived. The analysis indicates that the model exhibits two equilibrium points: A disease-free equilibrium and an endemic equilibrium. The local asymptotic stability of each equilibrium point is examined using the Routh-Hurwitz criterion. Additionally, by employing Lyapunov functionals and applying LaSalle's invariance principle, the global stability of the equilibrium points is demonstrated. The main conclusion is that under appropriate conditions, if        R    0    α    <  1, then the disease will eventually disappear, whereas if        R    0    α    >  1, then it will persist. Finally, the model is utilized to predict and control of HIV/AIDS transmission in Mexico, thereby highlighting the role of mutural preventive measures adopted by susceptible individuals and HIV-infected individuals in reducing disease spread. Simulations are performed to confirm the theoretical validity and practical significance of the model.}
}