scholarly journals Analysis of Dynamical Behavior for Epidemic Disease COVID-19 with Application

2021 ◽  
Vol 12 (4) ◽  
pp. 568-577
Author(s):  
Dr. Maysoon M. Aziz, Et. al.
Keyword(s):  
Time Series ◽  
Linear System ◽  
Power Spectrum ◽  
Dynamical Behavior ◽  
Simulated Data ◽  
Real Data ◽  
Sir Model ◽  
Epidemic Disease ◽  
The World ◽  
Non Linear System

In this paper, we will use the differential equations of the SIR model as a non-linear system, by using the Runge-Kutta numerical method to calculate simulated values for known epidemiological diseases related to the time series including the epidemic disease COVID-19, to obtain hypothetical results and compare them with the dailyreal statisticals of the disease for counties of the world and to know the behavior of this disease through mathematical applications, in terms of stability as well as chaos in many applied methods. The simulated data was obtained by using Matlab programms, and compared between real data and simulated datd were well compatible and with a degree of closeness. we took the data for Italy as an application.  The results shows that this disease is unstable, dissipative and chaotic, and the Kcorr of it equal (0.9621), ,also the power spectrum system was used as an indicator to clarify the chaos of the disease, these proves that it is a spread,outbreaks,chaotic and epidemic disease .

scholarly journals Spread of Epidemic Disease on Edge-Weighted Graphs from a Database: A Case Study of COVID-19

2021 ◽  
Vol 18 (9) ◽  
pp. 4432
Author(s):  
Ronald Manríquez ◽  
Camilo Guerrero-Nancuante ◽  
Felipe Martínez ◽  
Carla Taramasco
Keyword(s):  
Public Health ◽  
Infectious Diseases ◽  
Preventive Measures ◽  
Weighted Graph ◽  
Real Data ◽  
Sir Model ◽  
Weighted Graphs ◽  
Epidemic Disease ◽  
The Real

The understanding of infectious diseases is a priority in the field of public health. This has generated the inclusion of several disciplines and tools that allow for analyzing the dissemination of infectious diseases. The aim of this manuscript is to model the spreading of a disease in a population that is registered in a database. From this database, we obtain an edge-weighted graph. The spreading was modeled with the classic SIR model. The model proposed with edge-weighted graph allows for identifying the most important variables in the dissemination of epidemics. Moreover, a deterministic approximation is provided. With database COVID-19 from a city in Chile, we analyzed our model with relationship variables between people. We obtained a graph with 3866 vertices and 6,841,470 edges. We fitted the curve of the real data and we have done some simulations on the obtained graph. Our model is adjusted to the spread of the disease. The model proposed with edge-weighted graph allows for identifying the most important variables in the dissemination of epidemics, in this case with real data of COVID-19. This valuable information allows us to also include/understand the networks of dissemination of epidemics diseases as well as the implementation of preventive measures of public health. These findings are important in COVID-19’s pandemic context.

Dynamic Analysis of the Effect of Quitting Smoking Applications on Smoking Cessation

2020 ◽  
pp. 74-94
Author(s):  
A. George Maria Selvam ◽  
Mary Jacintha
Keyword(s):  
Time Series ◽  
Smoking Cessation ◽  
Linear System ◽  
Dynamic Analysis ◽  
Dynamical Analysis ◽  
Phase Portraits ◽  
System Of Differential Equations ◽  
Bifurcation Diagrams ◽  
Quitting Smoking ◽  
Non Linear System

In this chapter, the authors considered a smoking cessation model formulated with a non-linear system of differential equations and obtained the continuous fractional order model and through discretization its discrete form to study the effectiveness of quitting smoking applications in giving up smoking. The existence of smoking free equilibria and smoking present equilibria are discussed, and the dynamical analysis of these two equilibria is put forward with the assistance of the smoking generation number. The numerical simulations aided by time series, phase portraits, and bifurcation diagrams confirm the results that are obtained analytically.

ON THE RELIABILITY OF THE SURROGATE DATA TEST FOR NONLINEARITY IN THE ANALYSIS OF NOISY TIME SERIES

2001 ◽  
Vol 11 (07) ◽  
pp. 1881-1896 ◽  
Author(s):  
D. KUGIUMTZIS
Keyword(s):  
Time Series ◽  
Null Hypothesis ◽  
Volterra Series ◽  
Simulated Data ◽  
Real Data ◽  
Surrogate Data ◽  
Largest Lyapunov Exponent ◽  
Real World Data ◽  
Original Time ◽  
False Nearest Neighbors

In the analysis of real world data, the surrogate data test is often performed in order to investigate nonlinearity in the data. The null hypothesis of the test is that the original time series is generated from a linear stochastic process possibly undergoing a nonlinear static transform. We argue against reported rejection of the null hypothesis and claims of evidence of nonlinearity based on a single nonlinear statistic. In particular, two schemes for the generation of surrogate data are examined, the amplitude adjusted Fourier transform (AAFT) and the iterated AAFT (IAFFT) and many nonlinear discriminating statistics are used for testing, i.e. the fit with the Volterra series of polynomials and the fit with local average mappings, the mutual information, the correlation dimension, the false nearest neighbors, the largest Lyapunov exponent and simple nonlinear averages (the three point autocorrelation and the time reversal asymmetry). The results on simulated data and real data (EEG and exchange rates) suggest that the test depends on the method and its parameters, the algorithm generating the surrogate data and the observational data of the examined process.

scholarly journals Local Functional Coefficient Autoregressive Model for Multistep Prediction of Chaotic Time Series

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
Liyun Su ◽  
Chenlong Li
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Chaos Theory ◽  
Nearest Neighbor ◽  
Simulated Data ◽  
Real Data ◽  
Chaotic Time Series ◽  
Dimensional Phase Space ◽  
Local Functional ◽  
Functional Coefficient

A new methodology, which combines nonparametric method based on local functional coefficient autoregressive (LFAR) form with chaos theory and regional method, is proposed for multistep prediction of chaotic time series. The objective of this research study is to improve the performance of long-term forecasting of chaotic time series. To obtain the prediction values of chaotic time series, three steps are involved. Firstly, the original time series is reconstructed inm-dimensional phase space with a time delayτby using chaos theory. Secondly, select the nearest neighbor points by using local method in them-dimensional phase space. Thirdly, we use the nearest neighbor points to get a LFAR model. The proposed model’s parameters are selected by modified generalized cross validation (GCV) criterion. Both simulated data (Lorenz and Mackey-Glass systems) and real data (Sunspot time series) are used to illustrate the performance of the proposed methodology. By detailed investigation and comparing our results with published researches, we find that the LFAR model can effectively fit nonlinear characteristics of chaotic time series by using simple structure and has excellent performance for multistep forecasting.

Time-Rescaling Regression Method for Exponential Decay Time Series Predictions

2021 ◽  
Author(s):  
Masaru Shintani ◽  
Ken Umeno
Keyword(s):  
Time Series ◽  
Exponential Decay ◽  
Decay Time ◽  
Real Data ◽  
Regression Method ◽  
Random Numbers ◽  
Time Axis ◽  
Exponential Functions ◽  
Exponential Law ◽  
The World

Abstract The exponential law has been discovered in various systems around the world. In this study, we introduce two existing and one proposed analytical method for exponential decay time-series predictions. The proposed method is given by a linear regression that is based on rescaling the time axis in terms of exponential decay laws. We confirm that the proposed method has a higher prediction accuracy than existing methods by performance evaluation using random numbers and verification using actual data. The proposed method can be used for analyzing real data modeled with exponential functions, which are ubiquitous in the world.

Graphic analysis and multifractal on percolation-based return interval series

2015 ◽  
Vol 26 (12) ◽  
pp. 1550137 ◽  
Author(s):  
A. Q. Pei ◽  
J. Wang
Keyword(s):  
Time Series ◽  
Financial Time Series ◽  
Simulated Data ◽  
Small World ◽  
Real Data ◽  
Fluctuation Analysis ◽  
Multifractal Detrended Fluctuation Analysis ◽  
The Real ◽  
Return Interval ◽  
Financial Time

A financial time series model is developed and investigated by the oriented percolation system (one of the statistical physics systems). The nonlinear and statistical behaviors of the return interval time series are studied for the proposed model and the real stock market by applying visibility graph (VG) and multifractal detrended fluctuation analysis (MF-DFA). We investigate the fluctuation behaviors of return intervals of the model for different parameter settings, and also comparatively study these fluctuation patterns with those of the real financial data for different threshold values. The empirical research of this work exhibits the multifractal features for the corresponding financial time series. Further, the VGs deviated from both of the simulated data and the real data show the behaviors of small-world, hierarchy, high clustering and power-law tail for the degree distributions.

scholarly journals Artificial Detection of Lower-Frequency Periodicity in Climatic Studies by Wavelet Analysis Demonstrated on Synthetic Time Series

2019 ◽  
Vol 58 (9) ◽  
pp. 2077-2086 ◽  
Author(s):  
Assaf Hochman ◽  
Hadas Saaroni ◽  
Felix Abramovich ◽  
Pinhas Alpert
Keyword(s):  
Time Series ◽  
Wavelet Analysis ◽  
Power Spectrum ◽  
Low Frequency ◽  
Real Data ◽  
Careful Analysis ◽  
Wavelet Power Spectrum ◽  
Natural Oscillations ◽  
Local Singularity ◽  
Climatic Time Series

AbstractThe continuous wavelet transform (CWT) is a frequently used tool to study periodicity in climate and other time series. Periodicity plays a significant role in climate reconstruction and prediction. In numerous studies, the use of CWT revealed dominant periodicity (DP) in climatic time series. Several studies suggested that these “natural oscillations” would even reverse global warming. It is shown here that the results of wavelet analysis for detecting DPs can be misinterpreted in the presence of local singularities that are manifested in lower frequencies. This may lead to false DP detection. CWT analysis of synthetic and real-data climatic time series, with local singularities, indicates a low-frequency DP even if there is no true periodicity in the time series. Therefore, it is argued that this is an inherent general property of CWT. Hence, applying CWT to climatic time series should be reevaluated, and more careful analysis of the entire wavelet power spectrum is required, with a focus on high frequencies as well. A conelike shape in the wavelet power spectrum most likely indicates the presence of a local singularity in the time series rather than a DP, even if the local singularity has an observational or a physical basis. It is shown that analyzing the derivatives of the time series may be helpful in interpreting the wavelet power spectrum. Nevertheless, these tests are only a partial remedy that does not completely neutralize the effects caused by the presence of local singularities.

scholarly journals An Eye on the Future of COVID’19: Prediction of Likely Positive Cases and Fatality in India over A 30 Days Horizon using Prophet Model

2020 ◽  
pp. 1-20
Author(s):  
Vatsal Tulshyan ◽  
Dolly Sharma ◽  
Mamta Mittal
Keyword(s):  
Experimental Study ◽  
Time Series ◽  
Data Analysis ◽  
Programming Language ◽  
Missing Values ◽  
Mainland China ◽  
Real Data ◽  
Analysis Model ◽  
Data Prediction ◽  
The World

ABSTRACT Background: The coronavirus disease pandemic was initiated in Wuhan province of mainland China in December 2019 and has spread over the world. Objective: This study analyses the effects of COVID 19 based on Likely Positive Cases and fatality in India during and after the lockdown period from 24 March 2020 to 24 May 2020. Methods: Python has been used as the main programming language for data analysis and forecasting using the Prophet Model, a time series analysis model. The dataset has been preprocessed by grouping together the days for total numbers of cases and deaths on few selected dates and removed missing values present in some states. Results: The Prophet model performs better in terms of precision on the real data. Prediction depicts that during the lockdown, the total cases were rising but in a controlled manner with an accuracy of 87%. After the relaxation of lockdown rules, the predictions have shown an obstreperous situation with an accuracy of 60%. Conclusion: The resilience could have been better if the lockdown with strict norms was continued without much relaxation. The situation after lockdown has been found to be uncertain as observed by the experimental study conducted in this work.

scholarly journals SEED-G: Simulated EEG Data Generator for Testing Connectivity Algorithms

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3632
Author(s):  
Alessandra Anzolin ◽  
Jlenia Toppi ◽  
Manuela Petti ◽  
Febo Cincotti ◽  
Laura Astolfi
Keyword(s):  
Time Series ◽  
Brain Activity ◽  
Simulated Data ◽  
Ground Truth ◽  
Real Data ◽  
Connectivity Pattern ◽  
Data Simulation ◽  
Eeg Data ◽  
Data Generator ◽  
Wide Range

EEG signals are widely used to estimate brain circuits associated with specific tasks and cognitive processes. The testing of connectivity estimators is still an open issue because of the lack of a ground-truth in real data. Existing solutions such as the generation of simulated data based on a manually imposed connectivity pattern or mass oscillators can model only a few real cases with limited number of signals and spectral properties that do not reflect those of real brain activity. Furthermore, the generation of time series reproducing non-ideal and non-stationary ground-truth models is still missing. In this work, we present the SEED-G toolbox for the generation of pseudo-EEG data with imposed connectivity patterns, overcoming the existing limitations and enabling control of several parameters for data simulation according to the user’s needs. We first described the toolbox including guidelines for its correct use and then we tested its performances showing how, in a wide range of conditions, datasets composed by up to 60 time series were successfully generated in less than 5 s and with spectral features similar to real data. Then, SEED-G is employed for studying the effect of inter-trial variability Partial Directed Coherence (PDC) estimates, confirming its robustness.

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