Dynamical Behaviors of an SIR Epidemic Model with Discrete Time

Li, Bo; Eskandari, Zohreh; Avazzadeh, Z.

doi:10.3390/fractalfract6110659

Cited by 35 publications

(17 citation statements)

References 39 publications

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“…Currently, fractional calculus has the focus of researchers due to its vast applications in mathematical physics [18,19], bifurcation [20][21][22], and many more [23][24][25][26]. In the future, we will try to solve fractional order boundary values using the double Sawi transform.…”

Section: Discussionmentioning

confidence: 99%

Double Sawi Transform: Theory and Applications to Boundary Values Problems

et al. 2023

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Symmetry can play an important role in the study of boundary value problems, which are a type of problem in mathematics that involves finding the solutions to differential equations subject to given boundary conditions. Integral transforms play a crucial role in solving ordinary differential equations (ODEs), partial differential equations (PDEs), and integral equations. This article focuses on extending a single-valued Sawi transform to a double-valued ST, which we call the double Sawi (DS) transform. We derive some fundamental features and theorems for the proposed transform. Finally, we study the applications of the proposed transform by solving some boundary value problems such as the Fourier heat equation and the D’Alembert wave equation.

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Section: Discussionmentioning

confidence: 99%

Double Sawi Transform: Theory and Applications to Boundary Values Problems

et al. 2023

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“…Case I: In this case, we consider the QSO W 1 ; then, for the corresponding genetic algebra A 1 , the Proof. Let W 1 be given by (15) with the parameters a i , b i , c i , and W 2 be given by ( 16) with the following parameters a i , b i , c i , such that…”

Section: Associativitymentioning

confidence: 99%

“…Theorem 5. Let A 1 be the genetic algebra generated by W 1 (15) with c i = 0, ∀i ∈ {1, 2, 3}. Then, the following statements hold.…”

Section: Derivationsmentioning

confidence: 99%

“…The reader is referred to [12] for a self-contained exposition of the recent achievements and open problems in the theory of QSOs. QSOs find applications as discrete-time dynamical systems in various fields, including economics, epidemiology, and social sciences [13][14][15][16][17]. They are valuable tools for analyzing and predicting the behavior of complex systems that undergo discrete changes at fixed time intervals.…”

Section: Introductionmentioning

confidence: 99%

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Genetic Algebras Associated with ξ(a)-Quadratic Stochastic Operators

Mukhamedov,

Qaralleh,

Qaisar

et al. 2023

Entropy

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The present paper deals with a class of ξ(a)-quadratic stochastic operators, referred to as QSOs, on a two-dimensional simplex. It investigates the algebraic properties of the genetic algebras associated with ξ(a)-QSOs. Namely, the associativity, characters and derivations of genetic algebras are studied. Moreover, the dynamics of these operators are also explored. Specifically, we focus on a particular partition that results in nine classes, which are further reduced to three nonconjugate classes. Each class gives rise to a genetic algebra denoted as Ai, and it is shown that these algebras are isomorphic. The investigation then delves into analyzing various algebraic properties within these genetic algebras, such as associativity, characters, and derivations. The conditions for associativity and character behavior are provided. Furthermore, a comprehensive analysis of the dynamic behavior of these operators is conducted.

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“…Caputo further generalized the Caputo-Fabrizio derivative into another Atangana-Baleanu fractional derivative, involving the Mittag-Leffler function [31]. The authors of [32] studied the mathematical model of smoking with the Caputo-Fabrizio operator, and [33] investigated the SIR model. The choice among these operators depends on the specific characteristics of the system being modeled and the desired level of flexibility in the mathematical context [34].…”

Section: Introductionmentioning

confidence: 99%

Mathematical insights of social media addiction: fractal-fractional perspectives

Nadeem Anjam,

Tabassum,

Arshad

et al. 2024

Phys. Scr.

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The excessive use of social media has become a growing concern in the current century, with dependence on these platforms developing into a complex behavioral addiction. Addressing this issue requires the employment of well-directed and inclusive efforts. In pursuit of continuous development in existent strategies, this article presents a non-linear deterministic mathematical model that encapsulates the dynamics of social media addiction within a population. The proposed model incorporates the fractal-fractional order derivative in the sense of the Caputo operator. The objectives of this research are attained by groping the dynamics of the social media addiction model through the stratification of the population into five compartments: susceptible individuals, exposed individuals, addicted individuals, recovery individuals, and those who have quit using social media. The validity of the devised model is established by proving the existence and uniqueness of the solution within the framework of the fixed-point theory. The Ulam-Hyer's stability is established through nonlinear functional analysis, perturbing the problem with a small factor. Utilizing the Adam Bashforth numerical scheme, we obtain numerical solutions, which we validate through MATLAB simulations. \textcolor{red}{Additionally, we explore the application of artificial neural networks (ANNs) to approximate solutions, presenting a significant innovation in this domain. We propose the adoption of this novel method for solving integral equations that elucidate the dynamics of social media addiction, surpassing traditional numerical methods. Numerical results are illustrated across various fractional orders and fractal dimensions, with comparisons made against integer orders. Our study indicates that ANN outperforms the Adams-Bashforth algorithm, offering a dependable approach to problem-solving.} Throughout the article, we underscore the competitive advantage of our proposed strategy, providing a more nuanced understanding of the complex dynamics outlined in the model.

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Dynamical Behaviors of an SIR Epidemic Model with Discrete Time

Cited by 35 publications

References 39 publications

Double Sawi Transform: Theory and Applications to Boundary Values Problems

Double Sawi Transform: Theory and Applications to Boundary Values Problems

Genetic Algebras Associated with ξ(a)-Quadratic Stochastic Operators

Mathematical insights of social media addiction: fractal-fractional perspectives

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