A New Incommensurate Fractional-Order Discrete COVID-19 Model with Vaccinated Individuals Compartment

Dababneh, Amer; Djenina, Noureddine; Ouannas, Adel; Grassi, Giuseppe; Batiha, Iqbal M.; Jebril, Iqbal H.

doi:10.3390/fractalfract6080456

Cited by 25 publications

(9 citation statements)

References 30 publications

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“…Modeling infectious illnesses is a fascinating area of mathematical biology. The models give a clear framework for understanding biological systems and their infections [25]- [26]. Thus, the development of a nonlinear system of ODE, which served as the basis for SIR and SEIR, marked the beginning of compartmental epidemic modeling [27].…”

Section: Mathematical Model Of Sirmentioning

confidence: 99%

Identification and Control of Epidemic Disease Based Neural Networks and Optimization Technique

Abougarair,

Elwefati

2023

IJRCS

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Developing effective strategies to contain the spread of infectious diseases, particularly in the case of rapidly evolving outbreaks like COVID-19, remains a pressing challenge. The Susceptible-Infected-Recovery (SIR) model, a fundamental tool in epidemiology, offers insights into disease dynamics. The SIR system exhibits complex nonlinear relationships between the input variables (e.g., population, infection rate, recovery rate) and the output variables (e.g., the number of infected individuals over time). We employ Recurrent Neural Networks (RNNs) to model the SIR system due to their ability to capture sequential dependencies and handle time-series data effectively. RNNs, with their ability to model nonlinear functions, can capture these intricate relationships, enabling accurate predictions and understanding of the dynamics of the system. Additionally, we apply the Pontryagin Minimum Principle (PMP) based different control strategies to formulate an optimal control approach aimed at maximizing the recovery rate while minimizing the number of affected individuals and achieving a balance between minimizing costs and satisfying constraints. This can include optimizing vaccination strategies, quarantine measures, treatment allocation, and resource allocation. The findings of this research indicate that the proposed modeling and control approach shows potential for a comprehensive analysis of viral spread, providing valuable insights and strategies for disease management on a global level. By integrating epidemiological modeling with intelligent control techniques, we contribute to the ongoing efforts aimed at combating infectious diseases on a larger scale.

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Section: Mathematical Model Of Sirmentioning

confidence: 99%

Identification and Control of Epidemic Disease Based Neural Networks and Optimization Technique

Abougarair,

Elwefati

2023

IJRCS

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“…Fractional chaotic behaviors are extensively seen in both social and natural sciences, attracting considerable interest from various domains. In recent years, discrete-time fractional calculus has attracted much interest due to its significance in real-world challenges [19][20][21][22][23][24][25][26]. These studies have reflected that the system's behavior is highly dependent on the chosen fractional order, showcasing its non-linear and complex nature, which makes it a fascinating subject of study in the field of fractional dynamics.…”

Section: Introductionmentioning

confidence: 99%

On Chaos and Complexity Analysis for a New Sine-Based Memristor Map with Commensurate and Incommensurate Fractional Orders

Hamadneh,

Abbes,

Al-Tarawneh

et al. 2023

Mathematics

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In this study, we expand a 2D sine map via adding the discrete memristor to introduce a new 3D fractional-order sine-based memristor map. Under commensurate and incommensurate orders, we conduct an extensive exploration and analysis of its nonlinear dynamic behaviors, employing diverse numerical techniques, such as analyzing Lyapunov exponents, visualizing phase portraits, and plotting bifurcation diagrams. The results emphasize the sine-based memristor map’s sensitivity to fractional-order parameters, resulting in the emergence of distinct and diverse dynamic patterns. In addition, we employ the sample entropy (SampEn) method and C0 complexity to quantitatively measure complexity, and we also utilize the 0–1 test to validate the presence of chaos in the proposed fractional-order sine-based memristor map. Finally, MATLAB simulations are be executed to confirm the results provided.

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“…Not only that, but discrete models have a unique physical process. [18][19][20][21][22]. In particular, infectious illness data are not continuous; however, they cover a specific time period.…”

Section: Introductionmentioning

confidence: 99%

On Stability of a Fractional Discrete Reaction–Diffusion Epidemic Model

Alsayyed,

Hioual,

Gharib

et al. 2023

Fractal Fract

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This paper considers the dynamical properties of a space and time discrete fractional reaction–diffusion epidemic model, introducing a novel generalized incidence rate. The linear stability of the equilibrium solutions of the considered discrete fractional reaction–diffusion model has been carried out, and a global asymptotic stability analysis has been undertaken. We conducted a global stability analysis using a specialized Lyapunov function that captures the system’s historical data, distinguishing it from the integer-order version. This approach significantly advanced our comprehension of the complex stability properties within discrete fractional reaction–diffusion epidemic models. To substantiate the theoretical underpinnings, this paper is accompanied by numerical examples. These examples serve a dual purpose: not only do they validate the theoretical findings, but they also provide illustrations of the practical implications of the proposed discrete fractional system.

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A New Incommensurate Fractional-Order Discrete COVID-19 Model with Vaccinated Individuals Compartment

Cited by 25 publications

References 30 publications

Identification and Control of Epidemic Disease Based Neural Networks and Optimization Technique

Identification and Control of Epidemic Disease Based Neural Networks and Optimization Technique

On Chaos and Complexity Analysis for a New Sine-Based Memristor Map with Commensurate and Incommensurate Fractional Orders

On Stability of a Fractional Discrete Reaction–Diffusion Epidemic Model

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