HIV/AIDS epidemic fractional-order model

Zafar, Zain Ul Abadin; Rehan, Kashif; Mushtaq, Muhammad

doi:10.1080/10236198.2017.1321640

Cited by 70 publications

(47 citation statements)

References 31 publications

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“…In the last several decades, the fractional calculus has been widely applied in numerous areas such as physics, mechanics, engineering, viscoelasticity, and biology. [23][24][25][26] Numerous scholars argued that it is more appropriate to depict the realistic phenomenon with fractional-order derivatives than integer-order ones since fractional-order derivatives can characterize the memory and hereditary properties of multifarious materials and processes. Recently, lots of outstanding results about fractional-order differential systems have been reported.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation analysis for a fractional‐order chemotherapy model with two different delays

Liao

et al. 2019

Math Methods in App Sciences

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Cancer is one of the most serious diseases in the world. The investigation on cancer treatment has attracted great attention from medical workers, mathematical researchers, and scholars in various fields. To understand the intrinsic characteristics of cancer, numerous scholars have established cancer treatment models and discussed the dynamical properties. However, the main work of many scholars only focuses on the integer-order cancer treatment models, while the study on fractional-order ones is quite a few. In the present article, on the basis of previous publications, we will put up a new fractional-order chemotherapy model with two different delays. By applying the stability theory and the Hopf bifurcation of fractional-order differential equations, we obtain a series of new stability criteria of the involved model and some sufficient conditions to ensure the existence of Hopf bifurcation of the involved model. Furthermore, the impact of two different delays and the fractional order on the stability and the emergence of Hopf bifurcation of involved model is presented.To illustrate the validity of analytical predictions, we perform computer simulations with Matlab software. The theoretical results in the manuscript are innovative and play an important role in cancer treatment.

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Section: Introductionmentioning

confidence: 99%

Bifurcation analysis for a fractional‐order chemotherapy model with two different delays

Liao

et al. 2019

Math Methods in App Sciences

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“…For example, the SIS model [27,69], the SIRS model [34,42], the SEIR model [35,39], the MSEIR model [28], among others. Epidemiological models have been successfully applied to the study of several diseases such as HIV/AIDS [52,68], Ebola [37,38], Influenza [63], Cancer [2], Dengue [55,64], Malaria [54,54], Salmonella infection [57], and Zika [49].…”

Section: Introductionmentioning

confidence: 99%

An epidemiological MSEIR model described by the Caputo fractional derivative

Almeida

Cruz

Martins

et al. 2018

Int. J. Dynam. Control

104

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A fractional MSEIR model is presented, involving the Caputo fractional derivative. The equilibrium points and the basic reproduction number are computed. An analysis of the local asymptotic stability at the disease free equilibrium is given. Finally, using Matlab, a numerical simulation of the varicella outbreak among Shenzhen school children, China, is carried out.Mathematics Subject Classification 2010: 26A33, 92D30, 37N25 .

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“…Baleanu et al investigated the anomalous diffusion expressed through fractional order differential operators in the Bloch‐Torrey equation . A fractional nonlinear mathematical model was proposed to analyze the spread of AIDS . The existence of positive solutions for discrete fractional systems was studied .…”

Section: Introductionmentioning

confidence: 99%

“…14 A frac-tional nonlinear mathematical model was proposed to analyze the spread of AIDS. 15 The existence of positive solutions for discrete fractional systems was studied. 16 In order to describe anomalous diffusion, the time-fractional DPL heat transfer models are discussed.…”

Section: Introductionmentioning

confidence: 99%

Efficient and accurate spectral method for the time‐fractional dual‐phase‐lag heat transfer model and its parameter estimation

Zheng

Jiang

Zhang

2019

Math Methods in App Sciences

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In the current paper, a heat transfer model is suggested based on a time‐fractional dual‐phase‐lag (DPL) model. We discuss the model in two parts, the direct problem and the inverse problem. Firstly, for solving it, the finite difference/Legendre spectral method is constructed. In the temporal direction, we employ the weighted and shifted Grünwald approximation, which can achieve second order convergence. In the spatial direction, the Legendre spectral method is used, it can obtain spectral accuracy. The stability and convergence are theoretically analyzed. For the inverse problem, the Bayesian method is used to construct an algorithm to estimate the four parameters for the model, namely, the time‐fractional order α, the time‐fractional order β, the delay time τT, and the relaxation time τq. Next, numerical experiments are provided to demonstrate the effectiveness of our scheme, with the values of τq and τT for processed meat employed. We also make a comparison with another method. The data obtained for the direct problem are used in the parameter estimation. The paper provides an accurate and efficient numerical method for the time‐fractional DPL model.

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HIV/AIDS epidemic fractional-order model

Cited by 70 publications

References 31 publications

Bifurcation analysis for a fractional‐order chemotherapy model with two different delays

Bifurcation analysis for a fractional‐order chemotherapy model with two different delays

An epidemiological MSEIR model described by the Caputo fractional derivative

Efficient and accurate spectral method for the time‐fractional dual‐phase‐lag heat transfer model and its parameter estimation

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