Stability Analysis of an Incommensurate Fractional-Order SIR Model

In this paper, we propose a modified fractional diffusive SEAIR epidemic model with a nonlinear incidence rate. A constructed model of fractional partial differential equations (PDEs) is more general than the corresponding model of fractional ordinary differential equations (ODEs). The Caputo fractional derivative is considered. Linear stability analysis of the disease-free equilibrium state of the epidemic model (ODEs) is presented by employing Routh–Hurwitz stability criteria. In order to solve this model, a fractional numerical scheme is proposed. The proposed scheme can be used to find conditions for obtaining positive solutions for diffusive epidemic models. The stability of the scheme is given, and convergence conditions are found for the system of the linearized diffusive fractional epidemic model. In addition to this, the deficiencies of accuracy and consistency in the nonstandard finite difference method are also underlined by comparing the results with the standard fractional scheme and the MATLAB built-in solver pdepe. The proposed scheme shows an advantage over the fractional nonstandard finite difference method in terms of accuracy. In addition, numerical results are supplied to evaluate the proposed scheme’s performance.

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“…Similarly, the difference equations for solving the remaining Equations ( 13)-( 16) are expressed as: Proof. We rewrite Equation (26) as:…”

Section: Proposed Fractional Schemementioning

confidence: 99%

“…A fractional model of susceptible-infected-recovered has been presented in [26]. The model considers the spread of infectious diseases.…”

Section: Introductionmentioning

confidence: 99%

A New Numerical Scheme for Time Fractional Diffusive SEAIR Model with Non-Linear Incidence Rate: An Application to Computational Biology

2022

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“…Chaos theory describes the behavior of certain dynamical systems whose state evolves with time and are highly sensitive to initial conditions. Because of the complexity of chaotic behavior in dynamical systems, it finds applications in a variety of fields, such as science, technology and medicine [8,9,10,11,12,13,14]. Studying chaotic systems can be a very valuable endeavor.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional fractional system with the stability condition and chaos control

Gholami

Ghaziani

Eskandari

2022

mmnsa

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A three-dimensional system is introduced in this paper and its local stability is analyzed. Our study establishes the validity and uniqueness of the linear feedback control for the proposed system and proves its existence and uniqueness. The numerical simulation algorithm described by Atanackovic and Stankovic is finally applied. The analytical results are analyzed and the dynamics of the system are explored in more detail.

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“…The fractional calculus is a generalization of the integer-order calculus and it provides more accurate results as compared to classical calculus. Hence, it is widely used in mathematical modelling of science and engineering, medical, and almost all area of education [39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60]. Nowadays, numbers of the fractional derivative are available to deal with real-world problems such as Caputo derivative, Caputo-Fabrizio derivative, Atangana-Baleneu derivative, Hilfer derivative, Weyl derivative, Conformable derivative and many more.…”

Section: Introductionmentioning

confidence: 99%

Chaos of calcium diffusion in Parkinson s infectious disease model and treatment mechanism via Hilfer fractional derivative

Joshi¹,

Jha²

2021

mmnsa

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Calcium is a vital element in our body and plays a crucial role to moderate the calcium signalling process. Calcium-dependent protein and flux through the sodium-calcium exchanger are also involved in signalling process to perform and execute necessary cellular activities. The loss or alteration in this cellular activity starts the early progress of Parkinson's disease. A mathematical calcium model is developed in the form of the Hilfer fractional reaction-diffusion equation to examine the calcium diffusion in the cells. The effect of calcium-dependent protein and flux through the sodium-calcium exchanger is incorporated in the model. The solution of the Hilfer fractional calcium model is obtained by using the Sumudu transform technique in the form of the Wright function and Mittag-Leffler function. The graphical results are obtained for the different amounts of proteins, presence, and absence of sodium-calcium exchanger, and various orders of Hilfer derivative. The obtained results show that the modified calcium model is a function of time, position, and Hilfer fractional derivative. Thus the modified Hilfer calcium model provides a rich physical interpretation of a calcium model as compared to the classical calcium model.

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Stability Analysis of an Incommensurate Fractional-Order SIR Model

Cited by 25 publications

References 18 publications

A New Numerical Scheme for Time Fractional Diffusive SEAIR Model with Non-Linear Incidence Rate: An Application to Computational Biology

A New Numerical Scheme for Time Fractional Diffusive SEAIR Model with Non-Linear Incidence Rate: An Application to Computational Biology

Three-dimensional fractional system with the stability condition and chaos control

Chaos of calcium diffusion in Parkinson s infectious disease model and treatment mechanism via Hilfer fractional derivative

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