Epidemic Dynamics of a Fractional-Order SIS Infectious Network Model

Liu, Na; Li, Yunliu; Sun, Junwei; Fang, Jie; Liu, Peng

doi:10.1155/2021/5518436

Cited by 3 publications

(1 citation statement)

References 26 publications

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“…The most prominent characteristic of the immune system in the human body is memory; therefore, it is more realistic to apply fractional differential equations to model the epidemic transmission dynamics. Applying fractional-order Lyapunov stability theory, researchers studied the stability of an HIV/AIDS fractional-order infectious disease model [22], COVID-19 fractional-order infectious disease model [23], and Caputo fractional-order SIS/SIR model [24,25]. Meanwhile, a novel parameter estimation method based on improved particle swarm optimization was proposed [26], which was extended to various fractional infectious disease models.…”

Section: Introductionmentioning

confidence: 99%

Dynamics and Event-Triggered Impulsive Control of a Fractional-Order Epidemic Model with Time Delay

Liu,

Wang,

Lan

et al. 2023

Fractal Fract

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Due to the lack of timely protection measures against infectious diseases, or based on the particularity of the transmission of some infectious diseases and the time-varying connections between people, the transmission dynamics of infectious diseases in the information society are becoming more and more complex and changeable. A fractional-order epidemic mathematical model with network weighting and latency is proposed in this paper, and the stability near the disease-free equilibrium point and endemic equilibrium point are discussed separately. Subsequently, an event-triggered impulsive control strategy based on an infection rate threshold is put forward. By selecting the appropriate control gain, the Zeno phenomenon can be eliminated on the premise of ensuring the stability of the control error system. Finally, the theoretical results were validated numerically and some conclusions are presented. These findings contribute to future research on the limited-time event-triggered impulsive control of infectious diseases.

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Section: Introductionmentioning

confidence: 99%

Dynamics and Event-Triggered Impulsive Control of a Fractional-Order Epidemic Model with Time Delay

Liu,

Wang,

Lan

et al. 2023

Fractal Fract

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Fractal and fractional SIS model for syphilis data

Gabrick,

Sayari,

Souza

et al. 2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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This work studies the SIS model extended by fractional and fractal derivatives. We obtain explicit solutions for the standard and fractal formulations; for the fractional case, we study numerical solutions. As a real data example, we consider the Brazilian syphilis data from 2011 to 2021. We fit the data by considering the three variations of the model. Our fit suggests a recovery period of 11.6 days and a reproduction ratio (R0) equal to 6.5. By calculating the correlation coefficient (r) between the real data and the theoretical points, our results suggest that the fractal model presents a higher r compared to the standard or fractional case. The fractal formulation is improved when two different fractal orders with distinguishing weights are considered. This modification in the model provides a better description of the data and improves the correlation coefficient.

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Epidemic Dynamics of a Fractional-Order SIR Weighted Network Model and Its Targeted Immunity Control

et al. 2022

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With outbreaks of epidemics, an enormous loss of life and property has been caused. Based on the influence of disease transmission and information propagation on the transmission characteristics of infectious diseases, in this paper, a fractional-order SIR epidemic model is put forward on a two-layer weighted network. The local stability of the disease-free equilibrium is investigated. Moreover, a conclusion is obtained that there is no endemic equilibrium. Since the elderly and the children have fewer social tiers, a targeted immunity control that is based on age structure is proposed. Finally, an example is presented to demonstrate the effectiveness of the theoretical results. These studies contribute to a more comprehensive understanding of the epidemic transmission mechanism and play a positive guiding role in the prevention and control of some epidemics.

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Epidemic Dynamics of a Fractional-Order SIS Infectious Network Model

Cited by 3 publications

References 26 publications

Dynamics and Event-Triggered Impulsive Control of a Fractional-Order Epidemic Model with Time Delay

Dynamics and Event-Triggered Impulsive Control of a Fractional-Order Epidemic Model with Time Delay

Fractal and fractional SIS model for syphilis data

Epidemic Dynamics of a Fractional-Order SIR Weighted Network Model and Its Targeted Immunity Control

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