Dynamics of a Fractional Order HIV Infection Model with Specific Functional Response and Cure Rate

Boukhouima, Adnane; Hattaf, Khalid; Yousfi, Noura

doi:10.1155/2017/8372140

Cited by 44 publications

(48 citation statements)

References 19 publications

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“…According to Lemmas 5 and 6 in [51], one can deduce that the solutions of the fractionalorder system (3) are non-negative. Next, the boundedness of the solutions of the fractional-order system (3) is given.…”

Section: Non-negativity and Boundednessmentioning

confidence: 99%

Dynamical analysis of a fractional-order eco-epidemiological model with disease in prey population

et al. 2020

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A fractional-order eco-epidemiological model with disease in the prey population is formulated and analyzed. Mathematical analysis and numerical simulations are performed to clarify the characteristics of the proposed fractional-order model. The existence, uniqueness, non-negativity and boundedness of the solutions are proved. The local and global asymptotic stability of all equilibrium points are investigated. Finally, numerical simulations are conducted to illustrate the analytical results. The occurrence of Hopf bifurcations and transcritical bifurcations for the fractional-order eco-epidemiological model are demonstrated. It is observed that the fractional order has a stabilization effect and it may help to control the coexistence between susceptible prey, infected prey and predator populations.

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Section: Non-negativity and Boundednessmentioning

confidence: 99%

Dynamical analysis of a fractional-order eco-epidemiological model with disease in prey population

et al. 2020

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“…3 then the interior equilibrium E * is locally asymptotically stable. 3 and 0 < m < 1 then the interior equilibrium E * is locally asymptotically stable.…”

Section: Resultsmentioning

confidence: 98%

“…In this section, we perform extensive numerical computations of the fractional order system (3) for different fractional values of m (0 < m < 1) and also for m = 1 . We use Adams-type predictor corrector method (PECE) for the numerical solution of system (3). It is an effective method to give numerical solutions of both linear and nonlinear FODE [23,24].…”

Section: Numerical Simulationsmentioning

confidence: 99%

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Global stability of a Leslie-Gower-type fractional order tritrophic food chain model

Mondal¹,

Bairagi²,

'Guerekata³

2019

Fractional Differential Calculus

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Recently, the dynamical behaviors of a fractional order three species food chain model was studied by Alidousti and Ghahfarokhi (Nonlinear Dynamics, doi: org/10.1007/s11071-018-4663-6, 2018). They proved both the local and global asymptotic stability of all equilibrium points except the interior one. This work extends their work and gives proof of both the local and global stability analysis of the interior equilibrium point. Numerical examples are also provided to substantiate the analytical findings.Research of NB is supported by JU-RUSA 2.0.

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“…They observe, via numerical simulations, that when the derivative order is near to one, then the Caputo-Fabrizio non-integer order derivative reveals better absorbing characteristics. For other related works, see, e.g., [4,12,16,36,40,45,58].…”

Section: Introductionmentioning

confidence: 99%

Lyapunov functions for fractional-order systems in biology: Methods and applications

Boukhouima

Hattaf

Lotfi

et al. 2020

Chaos, Solitons & Fractals

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We prove new estimates of the Caputo derivative of order α ∈ (0, 1] for some specific functions. The estimations are shown useful to construct Lyapunov functions for systems of fractional differential equations in biology, based on those known for ordinary differential equations, and therefore useful to determine the global stability of the equilibrium points for fractional systems. To illustrate the usefulness of our theoretical results, a fractional HIV population model and a fractional cellular model are studied. More precisely, we construct suitable Lyapunov functionals to demonstrate the global stability of the free and endemic equilibriums, for both fractional models, and we also perform some numerical simulations that confirm our choices.

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Dynamics of a Fractional Order HIV Infection Model with Specific Functional Response and Cure Rate

Cited by 44 publications

References 19 publications

Dynamical analysis of a fractional-order eco-epidemiological model with disease in prey population

Dynamical analysis of a fractional-order eco-epidemiological model with disease in prey population

Global stability of a Leslie-Gower-type fractional order tritrophic food chain model

Lyapunov functions for fractional-order systems in biology: Methods and applications

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