文章基本信息

标题：A Caputo–Fabrizio fractional differential equation model for HIV/AIDS with treatment compartment
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作者：Elvin J. Moore ; Sekson Sirisubtawee ; Sanoe Koonprasert 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2019
卷号：2019
期号：1
页码：1-20
DOI：10.1186/s13662-019-2138-9
出版社：Hindawi Publishing Corporation
摘要：In recent years, many new definitions of fractional derivatives have been proposed and used to develop mathematical models for a wide variety of real-world systems containing memory, history, or nonlocal effects. The main purpose of the present paper is to develop and analyze a Caputo–Fabrizio fractional derivative model for the HIV/AIDS epidemic which includes an antiretroviral treatment compartment. The existence and uniqueness of the system of solutions of the model are established using a fixed-point theorem and an iterative method. The model is shown to have a disease-free and an endemic equilibrium point. Conditions are derived for the existence of the endemic equilibrium point and for the local asymptotic stability of the disease-free equilibrium point. The results confirm that the disease-free equilibrium point becomes increasingly stable as the fractional order is reduced. Numerical simulations are carried out using a three-step Adams–Bashforth predictor method for a range of fractional orders to illustrate the effects of varying the fractional order and to support the theoretical results.
关键词：Caputo–Fabrizio fractional derivative ; HIV/AIDS epidemic model ; Non-singularity ; Three-step fractional Adams–Bashforth scheme