The discrete fractional order difference applied to an epidemic model with indirect transmission

Coll, Carmen; Herrero, Alicia; Ginestar, D.; Sánchez, Elena

doi:10.1016/j.apm.2021.11.002

Cited by 10 publications

(6 citation statements)

References 29 publications

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“…Since fractional-order system has the property of time memory, establishing complex system using fractional calculus theory can greatly improve the ability of identification, design, and control of dynamic system. According to the needs of modeling, long memory system or short memory system can be used [12][13][14][15][16][17][18]. Based on the short memory fractional differential equations, Wu et al [19] proposed a short memory fractional-order model, and derived the global stability conditions of variable-order neural networks.…”

Section: Introductionmentioning

confidence: 99%

Stability and bifurcation control analysis of a delayed fractional-order eco-epidemiological system

Zhao

2022

Eur. Phys. J. Plus

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Considering the factor of artificial intervention in biological control, a delayed fractional eco-epidemiological system with an extended feedback controller is proposed. By using the digestion delay as bifurcation parameter, the stability and Hopf bifurcation are investigated, and the branching conditions are given. The system undergoes Hopf bifurcation, when the parameter passes through the critical value. In addition, it can be pointed out that the negative feedback gain and the feedback delay could affect the bifurcation critical value of the system. Therefore, the Hopf bifurcation can also be induced by taking the feedback delay as a bifurcation parameter. Finally, by plotting the solution curve of the system, the significance of the controller to the stability of the eco-epidemiological system is verified.

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Section: Introductionmentioning

confidence: 99%

Stability and bifurcation control analysis of a delayed fractional-order eco-epidemiological system

Zhao

2022

Eur. Phys. J. Plus

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“…Defnition 1 (see [18,49,50]). For a discrete function x(k) on N, the α-order Grünwald-Letnikov diference operator ∆ α is defned as follows:…”

Section: Mathematical Preliminariesmentioning

confidence: 99%

“…Diferential or diference equations are usually used as a powerful analytical tool to study complex behavior in economics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. However, this kind of model just considers what occurs in the present state but ignores past phases of the process, or what has occurred in earlier states [18]. In reality, in economic processes, these variables are afected not only by their current values but also by their previous values.…”

Section: Introductionmentioning

confidence: 99%

“…As an application, Xin et al [23] proposed a discrete fractional Cournot duopoly game to overcome the error caused by the discretization of the continuous fractional models. Moreover, based on the above model, some discrete fractional economic models had been proposed and studied successively [18,[42][43][44][45][46]. However, the current literature mainly focuses on deterministic Cournot oligopoly games and little focus on stochastic settings.…”

Section: Introductionmentioning

confidence: 99%

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A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control

Ran,

Zhou

2024

Complexity

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A stochastic discrete fractional Cournot duopoly game model with a unique interior Nash equilibrium is developed in this study. Some sufficient criteria of the Lyapunov stability in probability for the proposed model at the interior Nash equilibrium are derived using the Lyapunov theory. The proposed model’s finite time stability in probability is then investigated using a nonlinear feedback control approach at the interior Nash equilibrium. The stochastic Bellman theory is also used to explore the locally optimum control problem. Furthermore, bifurcation diagrams, time series, and the 0-1 test are used to investigate the chaotic dynamics of this model. Finally, numerical examples are given to illustrate the obtained results.

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“…Momani, et al proposed the fractional SIR epidemic model of childhood diseases [14]. Coll, et al proposed a discrete fractional order model to analyze the behavior of an epidemic process based on the discrete version of G-L fractional derivative operator [15]. However, there are few studies about malware propagation based on the fractional order have been discussed.…”

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confidence: 99%

Malware propagation model of fractional order, optimal control strategy and simulations

Zhou¹,

Liu²,

Zhu³

et al. 2023

Front. Phys.

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In this paper, an improved SEIR model of fractional order is investigated to describe the behavior of malware propagation in the wireless sensor network. Firstly, the malware propagation model of fractional order is established based on the classical SEIR epidemic theory, the basic reproductive number is obtained by the next-generation method and the stability condition of the model is also analyzed. Then, the inverse approach for the uncertainty propagation based on the discrete element method and least square algorithm is presented to determine the unknown parameters of the propagation process. Finally, the optimal control strategy is also discussed based on the adaptive model. Simulation results show the proposed model works better than the propagation model of integer order. The error of proposed model is smaller than integer order models.

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The discrete fractional order difference applied to an epidemic model with indirect transmission

Cited by 10 publications

References 29 publications

Stability and bifurcation control analysis of a delayed fractional-order eco-epidemiological system

Stability and bifurcation control analysis of a delayed fractional-order eco-epidemiological system

A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control

Malware propagation model of fractional order, optimal control strategy and simulations

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