scholarly journals Epidemic Dynamics of a Fractional-Order SIS Infectious Network Model

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Na Liu ◽  
Yunliu Li ◽  
Junwei Sun ◽  
Jie Fang ◽  
Peng Liu
Keyword(s):  
Fractional Order ◽  
Network Model ◽  
Large Scale ◽  
Equilibrium Points ◽  
Transmission Dynamics ◽  
Economic Losses ◽  
Epidemic Dynamics ◽  
Order Coefficient ◽  
The Stability ◽  
And Control

Outbreak and large-scale of the infectious diseases have caused enormous economic losses to all countries in the world. Constructing a network model which could reflect the transmission dynamics of the epidemics and investigating their transmission laws have a significant meaning in the precaution and control of the epidemics. In this article, a fractional-order SIS epidemic network model is proposed. First, an expression of the basic reproduction number is deduced. Second, applying the Lyapunov function, the stability of the equilibrium points about the infectious model is analyzed in detail. Finally, an example is present to verify the theoretical analysis. Furthermore, on account of the fractional-order coefficient, its influence on the transmission dynamics is also exhibited.

scholarly journals Dynamics Analysis and Control of a Five-Term Fractional-Order System

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Li-xin Yang ◽  
Xiao-jun Liu
Keyword(s):  
Fractional Order ◽  
Equilibrium Points ◽  
Fractional Order System ◽  
Phase Portraits ◽  
Order System ◽  
Bifurcation Diagrams ◽  
Compound Structure ◽  
Dynamical Properties ◽  
The Stability ◽  
And Control

This paper proposes a new fractional-order chaotic system with five terms. Firstly, basic dynamical properties of the fractional-order system are investigated in terms of the stability of equilibrium points, Jacobian matrices theoretically. Furthermore, rich dynamics with interesting characteristics are demonstrated by phase portraits, bifurcation diagrams numerically. Besides, the control problem of the new fractional-order system is discussed via numerical simulations. Our results demonstrate that the new fractional-order system has compound structure.

scholarly journals Network Dynamics of a Fractional-Order Phase-Locked Loop with Infinite Coexisting Attractors

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Anitha Karthikeyan ◽  
Karthikeyan Rajagopal
Keyword(s):  
Fractional Order ◽  
Large Scale ◽  
Equilibrium Points ◽  
Network Dynamics ◽  
Phase Locked Loop ◽  
Coexisting Attractors ◽  
Third Order ◽  
Large Scale Networks ◽  
The Stability ◽  
Multiple Coexisting Attractors

We have investigated a fractional-order phase-locked loop characterised by a third-order differential equation. The integer-order mathematical model of the phase-locked loop (PLL) is first converted to fractional order using the Caputo-Fabrizio method. The stability of the equilibrium points is discussed in detail in both parameter and fractional-order domain. The proposed fractional-order phase-locked loop (FOPLL) model shows multiple coexisting attractors which was not discussed in the earlier literature of PLL. The significance of these infinite coexisting attractors is that they exist in the operation region of the PLL between [−π,π] which increases the complexity of operation of the PLLs. Mainly when such FOPLLs are used in large-scale networks, the synchronisation of the FOPLLs becomes complicated and will result in unstable control conditions. Hence, studying the network dynamics of such FOPLLs is significant which motivates us to investigate the synchronisation phenomenon of the FOPLLs constructed in a square network. We could show that, because of the multiple coexisting attractors, the FOPLLs show various synchronisation phenomena, and more importantly in the chaotic region for lower fractional-order values, we could show that the FOPLLs are synchronised and this finding is very useful to completely analyse the FOPLL networks in high-frequency operations.

scholarly journals Chaotic behavior analysis and control of a toxin producing phytoplankton and zooplankton system based on linear feedback

Filomat ◽  
2018 ◽  
Vol 32 (11) ◽  
pp. 3779-3789 ◽  
Author(s):  
Yadong Liu ◽  
Wenjun Liu
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Linear Feedback ◽  
Linear Feedback Control ◽  
The Stability ◽  
And Control ◽  
Fractional Orders

In this paper, we study the dynamic behavior and control of the fractional-order nutrientphytoplankton-zooplankton system. First, we analyze the stability of the fractional-order nutrient-plankton system and get the critical stable value of fractional orders. Then, by applying the linear feedback control and Routh-Hurwitz criterion, we yield the sufficient conditions to stabilize the system to its equilibrium points. Finally, Under a modified fractional-order Adams-Bashforth-Monlton algorithm, we simulate the results respectively.

scholarly journals Establishment and lineage dynamics of the SARS-CoV-2 epidemic in the UK

Science ◽  
2021 ◽  
pp. eabf2946
Author(s):  
Louis du Plessis ◽  
John T. McCrone ◽  
Alexander E. Zarebski ◽  
Verity Hill ◽  
Christopher Ruis ◽  
...  
Keyword(s):  
Large Scale ◽  
Phylogenetic Analyses ◽  
Transmission Dynamics ◽  
Genetic Lineage ◽  
Size Dependent ◽  
Spatio Temporal ◽  
The Uk ◽  
Lineage Structure ◽  
And Control ◽  
Lineage Diversity

The UK’s COVID-19 epidemic during early 2020 was one of world’s largest and unusually well represented by virus genomic sampling. Here we reveal the fine-scale genetic lineage structure of this epidemic through analysis of 50,887 SARS-CoV-2 genomes, including 26,181 from the UK sampled throughout the country’s first wave of infection. Using large-scale phylogenetic analyses, combined with epidemiological and travel data, we quantify the size, spatio-temporal origins and persistence of genetically-distinct UK transmission lineages. Rapid fluctuations in virus importation rates resulted in >1000 lineages; those introduced prior to national lockdown tended to be larger and more dispersed. Lineage importation and regional lineage diversity declined after lockdown, while lineage elimination was size-dependent. We discuss the implications of our genetic perspective on transmission dynamics for COVID-19 epidemiology and control.

scholarly journals Development and evaluation of duplex TaqMan real-time PCR assay for detection and differentiation of wide-type and MGF505-2R gene-deleted African swine fever viruses

2020 ◽  
Author(s):  
zhenhua Guo ◽  
Kunpeng Li ◽  
Songlin Qiao ◽  
Xinxin Chen ◽  
Ruiguang Deng ◽  
...  
Keyword(s):  
Real Time ◽  
Real Time Pcr ◽  
Large Scale ◽  
Limit Of Detection ◽  
African Swine Fever ◽  
Economic Losses ◽  
Clinical Samples ◽  
Diagnosis Method ◽  
Pcr Method ◽  
And Control

Abstract Background: African swine fever (ASF) is the most important disease to the pigs and cause serious economic losses to the countries with large-scale swine production. Vaccines are recognized as the most useful tool to prevent and control ASF virus (ASFV) infection. Currently, the MGF505 and MGF360 gene-deleted ASFVs or combined with CD2v deletion were confirmed to be the most promising vaccine candidates. Thus, it is essential to develop a diagnosis method to discriminate wide-type strain from the vaccines used.Results: In this study, we established a duplex TaqMan real-time PCR based on the B646L gene and MGF505-2R gene. The sequence alignment showed that the targeted regions of primers and probes are highly conserved in the genotype II ASFVs. The duplex real-time assay can specifically detect B646L and MGF505-2R gene single or simultaneously without cross-reaction with other porcine viruses tested. The limit of detection was 5.8 copies and 3.0 copies for the standard plasmids containing B646L and MGF505-2R genes, respectively. Clinical samples were tested in parallel by duplex real-time PCR and a commercial ASFV detection kit. The detection results of these two assays against B646L gene were well consistent.Conclusion: We successfully developed and evaluated a duplex TaqMan real-time PCR method which can effectively distinguish the wide type and MGF505 gene-deleted ASFVs. It would be a useful tool for the clinical diagnosis and control of ASF.

scholarly journals A Fractional-Order Discrete Noninvertible Map of Cubic Type: Dynamics, Control, and Synchronization

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Xiaojun Liu ◽  
Ling Hong ◽  
Lixin Yang ◽  
Dafeng Tang
Keyword(s):  
Fractional Order ◽  
Initial Conditions ◽  
Dimensional Space ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
State Variables ◽  
Discrete Maps ◽  
The Stability ◽  
Control And Synchronization ◽  
Simultaneous Variation

In this paper, a new fractional-order discrete noninvertible map of cubic type is presented. Firstly, the stability of the equilibrium points for the map is examined. Secondly, the dynamics of the map with two different initial conditions is studied by numerical simulation when a parameter or a derivative order is varied. A series of attractors are displayed in various forms of periodic and chaotic ones. Furthermore, bifurcations with the simultaneous variation of both a parameter and the order are also analyzed in the three-dimensional space. Interior crises are found in the map as a parameter or an order varies. Thirdly, based on the stability theory of fractional-order discrete maps, a stabilization controller is proposed to control the chaos of the map and the asymptotic convergence of the state variables is determined. Finally, the synchronization between the proposed map and a fractional-order discrete Loren map is investigated. Numerical simulations are used to verify the effectiveness of the designed synchronization controllers.

scholarly journals Stability of Fractional Order Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Margarita Rivero ◽  
Sergei V. Rogosin ◽  
José A. Tenreiro Machado ◽  
Juan J. Trujillo
Keyword(s):  
Fractional Calculus ◽  
Fractional Order ◽  
State Of The Art ◽  
Point Of View ◽  
Fractional Order Systems ◽  
Short Period ◽  
Systems And Control ◽  
Different Types ◽  
The Stability ◽  
And Control

The theory and applications of fractional calculus (FC) had a considerable progress during the last years. Dynamical systems and control are one of the most active areas, and several authors focused on the stability of fractional order systems. Nevertheless, due to the multitude of efforts in a short period of time, contributions are scattered along the literature, and it becomes difficult for researchers to have a complete and systematic picture of the present day knowledge. This paper is an attempt to overcome this situation by reviewing the state of the art and putting this topic in a systematic form. While the problem is formulated with rigour, from the mathematical point of view, the exposition intends to be easy to read by the applied researchers. Different types of systems are considered, namely, linear/nonlinear, positive, with delay, distributed, and continuous/discrete. Several possible routes of future progress that emerge are also tackled.

CHAOS IN DIFFUSIONLESS LORENZ SYSTEM WITH A FRACTIONAL ORDER AND ITS CONTROL

2012 ◽  
Vol 22 (04) ◽  
pp. 1250088 ◽  
Author(s):  
YONG XU ◽  
RENCAI GU ◽  
HUIQING ZHANG ◽  
DONGXI LI
Keyword(s):  
Feedback Control ◽  
Control Problem ◽  
Fractional Order ◽  
Lorenz System ◽  
Equilibrium Points ◽  
Control Technique ◽  
Order System ◽  
System Parameters ◽  
Simulation Results ◽  
The Stability

This paper aims to investigate the phenomenon of Diffusionless Lorenz system with fractional-order. We discuss the stability of equilibrium points of the fractional-order system theoretically, and analyze the chaotic behaviors and typical bifurcations numerically. We find rich dynamics in fractional-order Diffusionless Lorenz system with appropriate fractional order and system parameters. Besides, the control problem of fractional-order Diffusionless Lorenz system is examined using feedback control technique, and simulation results show the effectiveness of the method.

scholarly journals Development and evaluation of duplex TaqMan real-time PCR assay for detection and differentiation of wide-type and MGF505-2R gene-deleted African swine fever viruses

2020 ◽  
Vol 16 (1) ◽  
Author(s):  
Zhenhua Guo ◽  
Kunpeng Li ◽  
Songlin Qiao ◽  
Xin-xin Chen ◽  
Ruiguang Deng ◽  
...  
Keyword(s):  
Real Time ◽  
Real Time Pcr ◽  
Large Scale ◽  
Limit Of Detection ◽  
African Swine Fever ◽  
Economic Losses ◽  
Clinical Samples ◽  
Diagnosis Method ◽  
Pcr Method ◽  
And Control

Abstract Background African swine fever (ASF) is the most important disease to the pigs and cause serious economic losses to the countries with large-scale swine production. Vaccines are recognized as the most useful tool to prevent and control ASF virus (ASFV) infection. Currently, the MGF505 and MGF360 gene-deleted ASFVs or combined with CD2v deletion were confirmed to be the most promising vaccine candidates. Thus, it is essential to develop a diagnosis method to discriminate wide-type strain from the vaccines used. Results In this study, we established a duplex TaqMan real-time PCR based on the B646L gene and MGF505-2R gene. The sequence alignment showed that the targeted regions of primers and probes are highly conserved in the genotype II ASFVs. The duplex real-time assay can specifically detect B646L and MGF505-2R gene single or simultaneously without cross-reaction with other porcine viruses tested. The limit of detection was 5.8 copies and 3.0 copies for the standard plasmids containing B646L and MGF505-2R genes, respectively. Clinical samples were tested in parallel by duplex real-time PCR and a commercial ASFV detection kit. The detection results of these two assays against B646L gene were well consistent. Conclusion We successfully developed and evaluated a duplex TaqMan real-time PCR method which can effectively distinguish the wide type and MGF505 gene-deleted ASFVs. It would be a useful tool for the clinical diagnosis and control of ASF.

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