On Fractional Order Dengue Epidemic Model

Alsulami, Hamed; El-Shahed, Moustafa; Nieto, Juan J.; Shammakh, Wafa

doi:10.1155/2014/456537

Cited by 60 publications

(40 citation statements)

References 16 publications

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“…It has many applications in the field of engineering and sciences, like heat conduction, electricity, control theory, and fractals . The applications of fractional calculus like in the anomalous electron transport in amorphous materials, the reaction kinetics of proteins, the di‐electrical . Caputo introduced a fractional derivative which is used for the conventional initial and boundary conditions related to the real‐world problem .…”

Section: Introductionmentioning

confidence: 99%

“…3 Examine the differential calculus to non-integer orders of derivatives that can be drawn back to Leibnitz. 4 Normally, the authors used integer models due to the unavailability of solutions for fractional differential equations. It is a major field in applied mathematics, economics, biology, chemistry, and signal processing.…”

Section: Introductionmentioning

confidence: 99%

“…3,5 The applications of fractional calculus like in the anomalous electron transport in amorphous materials, the reaction kinetics of proteins, the di-electrical. 4 Caputo introduced a fractional derivative which is used for the conventional initial and boundary conditions related to the real-world problem. 6 Baleanu et al reported new advances in fractional calculus and nanotechnology and associated issues in their monograph.…”

Section: Introductionmentioning

confidence: 99%

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Analysis and dynamical behavior of fractional‐order cancer model with vaccine strategy

et al. 2020

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In recent year, the world has witnessed the arrival of deadly diseases like cancer over all the global levels. To fight back this disease or control the spread, mankind relies on modeling and medicine to control, cure, and behavior of the cancer diseases. We developed the fractional‐order immunotherapy bladder cancer model and used the BCG vaccine for treatment by using the Caputo fractional derivative operator φɛ(0,1]. A mathematical model has four variables B,E, Ti, Tu which represent the vaccine for the immune system, effector cells, total population of affected, and unaffected cells, respectively. In this model, we have two cases according to the growth rate of cells. The fractional‐order system is stable in both cases and gives the solution infeasible region for uniqueness, positivity, and boundedness to illustrate the treatment of cancer. The effect of fractional parameter on our obtained solutions is presented, and a comparison is made with the classical ordinary derivative operator. It is worthy to observe that fractional derivatives show significant changes and memory effects as compared with ordinary derivatives to control the disease at the initial stage to overcome the risk of living with cancer.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analysis and dynamical behavior of fractional‐order cancer model with vaccine strategy

et al. 2020

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“…Also, fractional order models possess memory, fractional order differential equations give us a more realistic way to model the dengue system. Lately, they have been utilized to analyze a dengue plague prototype [16]. Regardless of the way that the operator of the non-integer is more complex than the traditional one, there occur numerical strategies for cracking systems of DEs which are nonlinear [17].…”

Section: Introductionmentioning

confidence: 99%

A non-integer order dengue internal transmission model

2018

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A non-linear mathematical model with non-integer order γ , 0 < γ ≤ 1, is used to analyze the dengue virus transmission in the human body. Both disease-free F 0 and endemic F * equilibria are calculated. Their stability is also described using the stability theorem of non-integer order. The threshold parameter R 0 demonstrates an important behavior in the stability of a considerable model. For R 0 < 1, the disease-free equilibrium (DFE) F 0 is an attractor. For R 0 > 1, F 0 is not stable, the endemic equilibrium (EE) F * exists, and it is an attractor. Numerical examples of the proposed model are also proven to study the behavior of the system.

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“…On the other hand the Caputo fractional derivative accepts initial conditions similar to the integer order systems. Therefore, Caputo fractional derivative is preferred for modeling physical systems [5,6,[14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Discrete-Time Fractional Optimal Control

Chiranjeevi

Biswas

2017

Mathematics

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Abstract:A formulation and solution of the discrete-time fractional optimal control problem in terms of the Caputo fractional derivative is presented in this paper. The performance index (PI) is considered in a quadratic form. The necessary and transversality conditions are obtained using a Hamiltonian approach. Both the free and fixed final state cases have been considered. Numerical examples are taken up and their solution technique is presented. Results are produced for different values of α.

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On Fractional Order Dengue Epidemic Model

Abstract: This paper deals with the fractional order dengue epidemic model. The stability of disease-free and positive fixed points is studied. Adams-Bashforth-Moulton algorithm has been used to solve and simulate the system of differential equations.

Cited by 60 publications

References 16 publications

Analysis and dynamical behavior of fractional‐order cancer model with vaccine strategy

Analysis and dynamical behavior of fractional‐order cancer model with vaccine strategy

A non-integer order dengue internal transmission model

Discrete-Time Fractional Optimal Control

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