scholarly journals Dynamical analysis of fractional-order of IVGTT glucose–insulin interaction

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mansoor H. Alshehri ◽  
Sayed Saber ◽  
Faisal Z. Duraihem
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Order ◽  
Euler Method ◽  
Dynamical Analysis ◽  
Order Model ◽  
Insulin Metabolism ◽  
Fractional Order Model ◽  
Proposed Model ◽  
Predictor Corrector ◽  
Tolerance Testing

Abstract This paper proposes a fractional-order model of glucose–insulin interaction. In Caputo’s meaning, the fractional derivative is defined. This model arises in Bergman’s minimal model, used to describe blood glucose and insulin metabolism, after intravenous tolerance testing. We showed that the established model has existence, uniqueness, non-negativity, and boundedness of fractional-order model solutions. The model’s local and global stability was investigated. The parametric conditions under which a Hopf bifurcation occurs in the positive steady state for a proposed model are studied. Moreover, we present a numerical treatment for solving the proposed fractional model using the generalized Euler method (GEM). The model’s local stability and Hopf bifurcation of the proposed model in sense of the GEM are presented. Finally, numerical simulations of the model using the Adam–Bashforth–Moulton predictor corrector scheme and the GEM have been presented to support our analytical results.

scholarly journals Dynamical analysis of fractional order model of immunogenic tumors

2016 ◽  
Vol 8 (7) ◽  
pp. 168781401665670 ◽  
Author(s):  
Sadia Arshad ◽  
Dumitru Baleanu ◽  
Jianfei Huang ◽  
Yifa Tang ◽  
Maysaa Mohamed Al Qurashi
Keyword(s):  
Fractional Order ◽  
Dynamical Analysis ◽  
Order Model ◽  
Fractional Order Model

A fractional-order model of HIV infection: Numerical solution and comparisons with data of patients

2014 ◽  
Vol 07 (04) ◽  
pp. 1450036 ◽  
Author(s):  
A. A. M. Arafa ◽  
S. Z. Rida ◽  
M. Khalil
Keyword(s):  
Fractional Order ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Real Data ◽  
Euler Method ◽  
Order Model ◽  
Fractional Order Model ◽  
Plasma Virus Load ◽  
Hiv 1

In this paper, a fractional-order model which describes the human immunodeficiency type-1 virus (HIV-1) infection is presented. Numerical solutions are obtained using a generalized Euler method (GEM) to handle the fractional derivatives. The fractional derivatives are described in the Caputo sense. We show that the model established in this paper possesses non-negative solutions. Comparisons between the results of the fractional-order model, the results of the integer model and the measured real data obtained from 10 patients during primary HIV-1 infection are presented. These comparisons show that the results of the fractional-order model give predictions to the plasma virus load of the patients better than those of the integer model.

scholarly journals A fractional-order love dynamical model with time delay for synergic couple : Stability analysis and Hopf bifurcation

2021 ◽  
Author(s):  
SANTOSHI PANIGRAHI ◽  
Sunita Chand ◽  
S Balamuralitharan
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Fractional Order ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Order Model ◽  
Fractional Order Model ◽  
The Stability ◽  
The Impact

We investigate the fractional order love dynamic model with time delay for synergic couples in this manuscript. The quantitative analysis of the model has been done where the asymptotic stability of the equilibrium points of the model have been analyzed. Under the impact of time delay, the Hopf bifurcation analysis of the model has been done. The stability analysis of the model has been studied with the reproduction number less than or greater than 1. By using Laplace transformation, the analysis of the model has been done. The analysis shows that the fractional order model with a time delay can sufficiently improve the components and invigorate the outcomes for either stable or unstable criteria. In this model, all unstable cases are converted to stable cases under neighbourhood points. For all parameters, the reproduction ranges have been described. Finally, to illustrate our derived results numerical simulations have been carried out by using MATLAB. Under the theoretical outcomes from parameter estimation, the love dynamical system is verified.

DYNAMICAL ANALYSIS OF FRACTIONAL ORDER ZIKV MODEL

2021 ◽  
Vol 10 (5) ◽  
pp. 2469-2481
Author(s):  
N.A. Hidayati ◽  
A. Suryanto ◽  
W.M. Kusumawinahyu
Keyword(s):  
Numerical Simulation ◽  
Equilibrium Point ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Dynamical Analysis ◽  
Stability Conditions ◽  
Order Model ◽  
Fractional Order Model ◽  
The Stability ◽  
S Model

The ZIKV model presented in this article is developed by modifying \cite{Bonyah2016}’s model. The classical order is changed into fractional order model. The equilibrium points of the model are determined and the stability conditions of each equilibrium point have been done using Routh-Hurwitz conditions. Numerical simulation is presented to verify the result of stability analysis result. Numerical simulation is also used to shows the effect of the order $\alpha$ to the stability of the model’s equilibrium point.

Dynamical Analysis of Fractional Order Model for Computer Virus Propagation with Kill Signals

2020 ◽  
Vol 21 (3-4) ◽  
pp. 239-247 ◽  
Author(s):  
Necati Özdemir ◽  
Sümeyra Uçar ◽  
Beyza Billur İskender Eroğlu
Keyword(s):  
Fractional Order ◽  
Existence And Uniqueness ◽  
Computer Network ◽  
Computer Virus ◽  
Dynamical Analysis ◽  
Model Parameters ◽  
Order Model ◽  
Virus Propagation ◽  
Fractional Order Model ◽  
Matlab Program

AbstractThe kill signals are alert about possible viruses that infect computer network to decrease the danger of virus propagation. In this work, we focus on a fractional-order SEIR-KS model in the sense of Caputo derivative to analyze the effects of kill signal nodes on the virus propagation. For this purpose, we first prove the existence and uniqueness of the model and give qualitative analysis. Then, we obtain the numerical solution of the model by using the Adams–Bashforth–Moulton algorithm. Finally, the effects of model parameters are demonstrated with graphics drawn by MATLAB program.

scholarly journals Dynamical Analysis of Approximate Solutions of HIV-1 Model with an Arbitrary Order

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Asma ◽  
Nigar Ali ◽  
Gul Zaman ◽  
Anwar Zeb ◽  
Vedat Suat Erturk ◽  
...  
Keyword(s):  
Fractional Order ◽  
Dynamical Behavior ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Dynamical Analysis ◽  
Order Model ◽  
Hiv Model ◽  
Fractional Order Model ◽  
Adomian Decomposition ◽  
Hiv 1

This article studies the dynamical behavior of the analytical solutions of the system of fraction order model of HIV-1 infection. For this purpose, first, the proposed integer order model is converted into fractional order model. Then, Laplace-Adomian decomposition method (L-ADM) is applied to solve this fractional order HIV model. Moreover, the convergence of this method is also discussed. It can be observed from the numerical solution that (L-ADM) is very simple and accurate to solve fraction order HIV model.

scholarly journals A Fractional-Order Model for HIV Dynamics in a Two-Sex Population

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Fatmawati ◽  
Endrik Mifta Shaiful ◽  
Mohammad Imam Utoyo
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Numerical Approach ◽  
Hiv And Aids ◽  
Order Model ◽  
Fractional Order Model ◽  
Severe Stage ◽  
The Stability ◽  
Immunodeficiency Syndrome ◽  
Predictor Corrector

Human Immunodeficiency Virus (HIV) is a virus that attacks or infects cells in the immune system that causes immune decline. Acquired Immunodeficiency Syndrome (AIDS) is the most severe stage of HIV infection. AIDS is the rapidly spreading and becoming epidemic diseases in the world of almost complete influence across the country. A mathematical model approach of HIV/AIDS dynamic is needed to predict the spread of the diseases in the future. In this paper, we presented a fractional-order model of the spread of HIV and AIDS diseases which incorporates two-sex population. The fractional derivative order of the model is in the interval (0,1]. We compute the basic reproduction number and prove the stability of the equilibriums of the model. The sensitivity analysis also is done to determine the important factor controlling the spread. Using the Adams-type predictor-corrector method, we then perform some numerical simulations for variation values of the order of the fractional derivative. Finally, the effects of various antiretroviral therapy (ART) treatments are studied and compared with numerical approach.

Bifurcation Analysis of Fractional Order Single Cell with Delay

2015 ◽  
Vol 25 (02) ◽  
pp. 1550020 ◽  
Author(s):  
Vedat Çelik
Keyword(s):  
Neural Networks ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Single Cell ◽  
Fractional Order ◽  
Bifurcation Analysis ◽  
Stability Criterion ◽  
Order Model ◽  
Bifurcation Points ◽  
Fractional Order Model

This paper presents the bifurcation analysis of fractional order model of delayed single cell which is proposed for delayed cellular neural networks with respect to the time delay τ. The bifurcation points, time delay τc, are determined by modified Mikhailov stability criterion for a range of fractional delayed cell order 0.3 ≤ q < 1. Numerical results obtained from Adams–Bashforth–Moulton method demonstrate that the supercritical Hopf bifurcation occurs in the system.

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