scholarly journals Nonlinear Dynamics and Chaos in a Fractional-Order HIV Model

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
Haiping Ye ◽  
Yongsheng Ding
Keyword(s):  
Fractional Order ◽  
Equation Model ◽  
Viral Diversity ◽  
Human Immune System ◽  
Order Model ◽  
Hiv Model ◽  
Interior Equilibrium ◽  
Infected Cells ◽  
The One ◽  
Predictor Corrector

We introduce fractional order into an HIV model. We consider the effect of viral diversity on the human immune system with frequency dependent rate of proliferation of cytotoxic T-lymphocytes (CTLs) and rate of elimination of infected cells by CTLs, based on a fractional-order differential equation model. For the one-virus model, our analysis shows that the interior equilibrium which is unstable in the classical integer-order model can become asymptotically stable in our fractional-order model and numerical simulations confirm this. We also present simulation results of the chaotic behaviors produced from the fractional-order HIV model with viral diversity by using an Adams-type predictor-corrector method.

scholarly journals Stability Analysis and Clinic Phenomenon Simulation of a Fractional-Order HBV Infection Model

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yongmei Su ◽  
Sinuo Liu ◽  
Shurui Song ◽  
Xiaoke Li ◽  
Yongan Ye
Keyword(s):  
Fractional Order ◽  
Equilibrium Points ◽  
Mass Action ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Infection Model ◽  
Order Model ◽  
Infected Cells ◽  
Set Up ◽  
Hbv Model

In this paper, a fractional-order HBV model was set up based on standard mass action incidences and quasisteady assumption. The basic reproductive number R0 and the cytotoxic T lymphocytes’ immune-response reproductive number R1 were derived. There were three equilibrium points of the model, and stable analysis of each equilibrium point was given with corresponding hypothesis about R0 or R1. Some numerical simulations were also given based on HBeAg clinical data, and the simulation showed that there existed positive logarithmic correlation between the number of infected cells and HBeAg, which was consistent with the clinical facts. The simulation also showed that the clinical individual differences should be reflected by the fractional-order model.

scholarly journals Stability of a fractional order harvested prey–predator model in the existence of infection in prey

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Subhashis Das ◽  
◽  
Sanat Mahato ◽  
Prasenjit Mahato
Keyword(s):  
Fractional Order ◽  
Equilibrium Points ◽  
Type I ◽  
Interior Equilibrium ◽  
Proposed Model ◽  
Different Types ◽  
Predator Model ◽  
Predictor Corrector ◽  
Uniqueness Criteria ◽  
Type Ii Functional Response

The growing relationship between prey and their predator is one of the important aspects in the field of ecology and mathematical biology. On the other hand, the utility of fractional calculus in different types of mathematical modelling have been applied extensively. In this paper, a fractional order prey–predator model is developed with the consideration of Holling type-I and Holling type-II functional response of the predator. As infection spreads through prey, the prey population is divided into two parts. In addition, we exploit the effect of harvesting to control the excessive spread of the infection. The existence and uniqueness criteria, the boundedness of the solution of the proposed model are investigated. A number of five possible equilibrium points of the proposed model are determined along with the feasibility conditions for each equilibrium points. The local stability at these equilibrium points and global stability at interior equilibrium point are investigated. Numerical simulation is presented with the help of modified Predictor-corrector method in MATLAB software to understand the dynamics of the proposed model.

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.

scholarly journals ITERATIVE METHOD APPLIED TO THE FRACTIONAL NONLINEAR SYSTEMS ARISING IN THERMOELASTICITY WITH MITTAG-LEFFLER KERNEL

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040040 ◽  
Author(s):  
WEI GAO ◽  
P. VEERESHA ◽  
D. G. PRAKASHA ◽  
BILGIN SENEL ◽  
HACI MEHMET BASKONUS
Keyword(s):  
Fractional Order ◽  
Nonlinear Differential Equations ◽  
Order Model ◽  
Science And Engineering ◽  
One Dimensional ◽  
Fractional Order Model ◽  
Analysis Scheme ◽  
Laplace Transform Technique ◽  
Homotopy Analysis ◽  
The One

In this paper, we study on the numerical solution of fractional nonlinear system of equations representing the one-dimensional Cauchy problem arising in thermoelasticity. The proposed technique is graceful amalgamations of Laplace transform technique with [Formula: see text]-homotopy analysis scheme and fractional derivative defined with Atangana–Baleanu (AB) operator. The fixed-point hypothesis is considered in order to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. In order to illustrate and validate the efficiency of the future technique, we consider three different cases and analyzed the projected model in terms of fractional order. Moreover, the physical behavior of the obtained solution has been captured in terms of plots for diverse fractional order, and the numerical simulation is demonstrated to ensure the exactness. The obtained results elucidate that the proposed scheme is easy to implement, highly methodical as well as accurate to analyze the behavior of coupled nonlinear differential equations of arbitrary order arisen in the connected areas of science and engineering.

scholarly journals An Investigation on Analytical Properties of Delayed Fractional Order HIV Model: A Case Study

2021 ◽  
Vol 16 (1) ◽  
pp. 57-85
Author(s):  
M. Pitchaimani ◽  
A. Saranya Devi
Keyword(s):  
Fractional Order ◽  
Hiv Transmission ◽  
Equation Model ◽  
Model Parameters ◽  
Hiv Model ◽  
Proposed Model ◽  
Positivity Of Solutions ◽  
The Stability ◽  
Delay Differential ◽  
Spread Of Infection

In this manuscript, we design a fractional order delay differential equation model for HIV transmission with the implementation of three distinct therapies for three different infectious stages. We investigate the positivity of solutions, analyze the stability properties, followed by Hopf bifurcation analysis. To probe the parameters that expedite the spread of infection, uncertainty and sensitivity analysis were performed. The numerical review was carried out to substantiate our theoretical results. Our proposed model parameters have been calibrated to fit yearly data from Afghanistan, Australia, France, Italy, Netherlands and New Zealand.

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.

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