scholarly journals A fractional order HIV/AIDS epidemic model with Mittag-Leffler kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Muhammad Aslam ◽  
Rashid Murtaza ◽  
Thabet Abdeljawad ◽  
Ghaus ur Rahman ◽  
Aziz Khan ◽  
...  
Keyword(s):  
Fractional Order ◽  
Existence And Uniqueness ◽  
Lagrange Interpolation ◽  
Infection Model ◽  
Order Model ◽  
Aids Epidemic ◽  
Fractional Order Model ◽  
Fixed Point Technique ◽  
The Stability ◽  
Hiv Aids

AbstractIn this article, we study a fractional order HIV/AIDS infection model with ABC-fractional derivative. The model is based on four classes of a population. The study includes the existence and uniqueness of solution, the stability analysis, and simulations. We utilize the fixed point technique for the existence and uniqueness analysis. The stability of the fractional order model is derived with the help of existing literature for the Hyers–Ulam stability. For the numerical computations, the Lagrange interpolation is utilized, and the simulations are obtained for specific parameters. The results are closer to the classical results for different orders.

HIV/AIDS epidemic fractional-order model

2017 ◽  
Vol 23 (7) ◽  
pp. 1298-1315 ◽  
Author(s):  
Zain Ul Abadin Zafar ◽  
Kashif Rehan ◽  
M. Mushtaq
Keyword(s):  
Fractional Order ◽  
Order Model ◽  
Aids Epidemic ◽  
Fractional Order Model ◽  
Hiv Aids

scholarly journals A Caputo–Fabrizio Fractional-Order Model of HIV/AIDS with a Treatment Compartment: Sensitivity Analysis and Optimal Control Strategies

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 610
Author(s):  
Hua Wang ◽  
Hadi Jahanshahi ◽  
Miao-Kun Wang ◽  
Stelios Bekiros ◽  
Jinping Liu ◽  
...  
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Disease Transmission ◽  
Sensitivity Analyses ◽  
Atraumatic Restorative Treatment ◽  
Order Model ◽  
Optimal Control Strategy ◽  
Aids Epidemic ◽  
Fractional Order Model ◽  
Hiv Aids

Although most of the early research studies on fractional-order systems were based on the Caputo or Riemann–Liouville fractional-order derivatives, it has recently been proven that these methods have some drawbacks. For instance, kernels of these methods have a singularity that occurs at the endpoint of an interval of definition. Thus, to overcome this issue, several new definitions of fractional derivatives have been introduced. The Caputo–Fabrizio fractional order is one of these nonsingular definitions. This paper is concerned with the analyses and design of an optimal control strategy for a Caputo–Fabrizio fractional-order model of the HIV/AIDS epidemic. The Caputo–Fabrizio fractional-order model of HIV/AIDS is considered to prevent the singularity problem, which is a real concern in the modeling of real-world systems and phenomena. Firstly, in order to find out how the population of each compartment can be controlled, sensitivity analyses were conducted. Based on the sensitivity analyses, the most effective agents in disease transmission and prevalence were selected as control inputs. In this way, a modified Caputo–Fabrizio fractional-order model of the HIV/AIDS epidemic is proposed. By changing the contact rate of susceptible and infectious people, the atraumatic restorative treatment rate of the treated compartment individuals, and the sexual habits of susceptible people, optimal control was designed. Lastly, simulation results that demonstrate the appropriate performance of the Caputo–Fabrizio fractional-order model and proposed control scheme are illustrated.

scholarly journals Dynamic Analysis of a Fractional-Order Model for Hepatitis B Virus with Holling II Functional Response

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Ruiqing Shi ◽  
Ting Lu ◽  
Cuihong Wang
Keyword(s):  
Hepatitis B Virus ◽  
Hepatitis B ◽  
Fractional Order ◽  
Reproduction Number ◽  
Sufficient Conditions ◽  
Order Model ◽  
Fractional Order Model ◽  
B Virus ◽  
The Stability ◽  
Holling Ii Functional Response

In this paper, a fractional-order model is constructed to describe the transmission of Hepatitis B Virus (HBV). Firstly, the existence and uniqueness of positive solutions are proved. Secondly, the basic reproduction number and the sufficient conditions for the existence of two equilibriums are obtained. Thirdly, the stability of equilibriums are analyzed. After that, some numerical simulations are performed to verify the theoretical prediction. Finally, a brief discussion is presented.

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.

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