Stability analysis and numerical solutions of fractional order HIV/AIDS model

被引：139

作者：

Khan, Aziz ^{[1
]}

Gomez-Aguilar, J. F. ^{[2
]}

Khan, Tahir Saeed ^{[1
]}

Khan, Hasib ^{[3
,4
]}

机构：

[1] Univ Peshawar, Dept Math, POB 25000, Khybar Pakhtunkhwa, Pakistan

[2] CONACyT Tecnol Nacl Mexico CENIDET, Interior Internado Palmira S-N, Cuernavaca 62490, Morelos, Mexico

[3] Hohai Univ, State Key Lab Hydrol Water Resources & Hydraul En, Nanjing 210098, Jiangsu, Peoples R China

[4] Shaheed Benazir Bhutto Univ, Dir Upper 18000, Khyber Pakhtunk, Pakistan

来源：

CHAOS SOLITONS & FRACTALS | 2019年 / 122卷

基金：

中国国家自然科学基金;

关键词：

Liouville-Caputo derivative; Atangana-Baleanu-Caputo derivative; Laplace transform; Sumudu transform; Fixed point theorem; Adams methods; VIRUS;

D O I：

10.1016/j.chaos.2019.03.022

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this work, we study the Fractional Order (FO) model HIV/AIDS involving the Liouville-Caputo and Atangana-Baleanu-Caputo derivatives. The generalized HIV/AIDS model enable and indicates that some infected specific move from symptomatic phase to the asymptomatic phase in all kind of analysis. Special iterative solutions were obtained by the use of Laplace and Sumudu transform. Existence, uniqueness of the solution and stability criteria for the FO model were obtained by fixed point theorem. For the numerical treatment of generalized HIV/AIDS model, we using Adams methods. Furthermore, the convergency of the numerical solutions were analyzed in detail. Finally, for results illustration numerical simulations are presented. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页码：119 / 128

页数：10

共 28 条

[1]

Al Basir Fahad, 2017, WSEAS Transactions on Mathematics, V16, P152

[2]

Alkahtani BST, 2016, CHAOS SOLITON FRACT, V89, P1

[3]

[Anonymous], 2008, Anthropology and Public Health: Bridging Differences in Culture and Society, DOI [10.1093/acprof:oso/9780195374643.001.0001, DOI 10.1093/ACPROF:OSO/9780195374643.001.0001]

[4] The effect of anti-viral drug treatment of human immunodeficiency virus type 1 (HIV-1) described by a fractional order model [J].

Arafa, A. A. M. ;

Rida, S. Z. ;

Khalil, M. .

APPLIED MATHEMATICAL MODELLING, 2013, 37 (04) :2189-2196

[5] Construction of nonstandard finite difference schemes for the SI and SIR epidemic models of fractional order [J].

Arenas, Abraham J. ;

Gonzalez-Parra, Gilberto ;

Chen-Charpentier, Benito M. .

MATHEMATICS AND COMPUTERS IN SIMULATION, 2016, 121 :48-63

[6] Blind in a commutative world: Simple illustrations with functions and chaotic attractors [J].

Atangana, Abdon .

CHAOS SOLITONS & FRACTALS, 2018, 114 :347-363

[7] Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties [J].

Atangana, Abdon .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2018, 505 :688-706

[8] Decolonisation of fractional calculus rules: Breaking commutativity and associativity to capture more natural phenomena [J].

Atangana, Abdon ;

Gomez-Aguilar, J. F. .

EUROPEAN PHYSICAL JOURNAL PLUS, 2018, 133 (04)

[9] Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order [J].

Atangana, Abdon ;

Koca, Ilknur .

CHAOS SOLITONS & FRACTALS, 2016, 89 :447-454

[10] NEW FRACTIONAL DERIVATIVES WITH NON-LOCAL AND NON-SINGULAR KERNEL Theory and Application to Heat Transfer Model [J].

Atangana, Abdon ;

Baleanu, Dumitru .

THERMAL SCIENCE, 2016, 20 (02) :763-769

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