scholarly journals Parameter Estimation for the One-Term (Multiterm) Fractional-Order SEIAR Models of Norovirus Outbreak

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Tianzeng Li ◽  
Yu Wang ◽  
Weiqiu Pan
Keyword(s):  
Inverse Problem ◽  
Parameter Estimation ◽  
Fractional Order ◽  
Numerical Solutions ◽  
Real Data ◽  
Estimation Methods ◽  
The Real ◽  
Infected People ◽  
Single Term ◽  
The Impact

In the paper, we use the Caputo fractional derivative to consider general single-term and multiterm fractional-order SEIAR models for the outbreak of Norovirus. Then, the inverse problem about parameter estimation for these fractional-order SEIAR models of the Norovirus outbreak is studied firstly. To provide the numerical solution of the single-term (or multiterm) fractional-order nonlinear differential equation, the GMMP scheme and Newton method are introduced. Then, we make use of the modified hybrid Nelder-Mead simplex search and particle swarm optimization (MH-NMSS-PSO) algorithm to obtain the fractional orders and parameters for these fractional-order SEIAR models of Norovirus outbreak. To guarantee the correctness and effectiveness of the methods, the data of a 2007 Norovirus outbreak in a middle school in one city is used as the real data to solve the inverse problem of the parameter estimation. With the new parameters, all numerical studies illustrate that the numerical solutions fit very well with the real data, which reveals that the single-term and multiterm fractional-order SEIAR models of Norovirus outbreak all can predict the number of the infectious people accurately. And it also shows that the GMMP scheme and the MH-NMSS-PSO method are efficient and valid for estimating the parameters of the single-term (or multiterm) fractional-order nonlinear equations. Then, we research the impact of changes in each parameter on the amount of infected humans I t when the remaining parameters are unchanged. All results of numerical simulation reveal that the single-term and multiterm fractional-order SEIAR model of Norovirus can provide better results than other models. And we also study the effect of the isolation on different days. The conclusion is obtained that the earlier the isolation is taken, the less the infected people are. Hence, for a fractional-order application in the SEIAR model of Norovirus outbreak, we establish the effective parameter estimation methods.

scholarly journals A fractional order epidemic model for the simulation of outbreaks of Ebola

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Weiqiu Pan ◽  
Tianzeng Li ◽  
Safdar Ali
Keyword(s):  
Numerical Solution ◽  
Root Mean Square ◽  
Fractional Order ◽  
Relative Error ◽  
Numerical Solutions ◽  
Real Data ◽  
Mean Square ◽  
Order Model ◽  
The Real ◽  
Fractional Orders

AbstractThe Ebola outbreak in 2014 caused many infections and deaths. Some literature works have proposed some models to study Ebola virus, such as SIR, SIS, SEIR, etc. It is proved that the fractional order model can describe epidemic dynamics better than the integer order model. In this paper, we propose a fractional order Ebola system and analyze the nonnegative solution, the basic reproduction number $R_{0}$ R 0 , and the stabilities of equilibrium points for the system firstly. In many studies, the numerical solutions of some models cannot fit very well with the real data. Thus, to show the dynamics of the Ebola epidemic, the Gorenflo–Mainardi–Moretti–Paradisi scheme (GMMP) is taken to get the numerical solution of the SEIR fractional order Ebola system and the modified grid approximation method (MGAM) is used to acquire the parameters of the SEIR fractional order Ebola system. We consider that the GMMP method may lead to absurd numerical solutions, so its stability and convergence are given. Then, the new fractional orders, parameters, and the root-mean-square relative error $g(U^{*})=0.4146$ g ( U ∗ ) = 0.4146 are obtained. With the new fractional orders and parameters, the numerical solution of the SEIR fractional order Ebola system is closer to the real data than those models in other literature works. Meanwhile, we find that most of the fractional order Ebola systems have the same order. Hence, the fractional order Ebola system with different orders using the Caputo derivatives is also studied. We also adopt the MGAM algorithm to obtain the new orders, parameters, and the root-mean-square relative error which is $g(U^{*})=0.2744$ g ( U ∗ ) = 0.2744 . With the new parameters and orders, the fractional order Ebola systems with different orders fit very well with the real data.

scholarly journals A fractional-order SEIHDR model for COVID-19 with inter-city networked coupling effects

2020 ◽  
Author(s):  
Zhenzhen Lu ◽  
Yongguang Yu ◽  
YangQuan Chen ◽  
Guojian Ren ◽  
Conghui Xu ◽  
...  
Keyword(s):  
Fractional Order ◽  
Numerical Solutions ◽  
Least Squares Method ◽  
Real Data ◽  
Order System ◽  
Coupling Effects ◽  
Order Model ◽  
The Real ◽  
Proposed Model ◽  
City Network

AbstractA novel coronavirus, designated as COVID-19, emerged in Wuhan, China, at the end of 2019. In this paper, a mathematical model is proposed to analyze the dynamic behavior of COVID-19. Based on inter-city networked coupling effects, a fractional-order SEIHDR system with the real-data from 23 January to 18 March, 2020 of COVID19 is discussed. Meanwhile, hospitalized individuals and the mortality rates of three types of individuals (exposed, infected and hospitalized) are firstly taken into account in the proposed model. And infectivity of individuals during incubation is also considered in this paper. By applying least squares method and predictor-correctors scheme, the numerical solutions of the proposed system in the absence of the inter-city network and with the inter-city network are stimulated by using the real-data from 23 January to 18 − m March, 2020 where m is equal to the number of prediction days. Compared with integer-order system (α = 0), the fractional-order model without network is validated to have a better fitting of the data on Beijing, Shanghai, Wuhan, Huanggang and other cities. In contrast to the case without network, the results indicate that the inter-city network system may be not a significant case to virus spreading for China because of the lock down and quarantine measures, however, it may have an impact on cities that have not adopted city closure. Meanwhile, the proposed model better fits the data from 24 February to 31, March in Italy, and the peak number of confirmed people is also predicted by this fraction-order model. Furthermore, the existence and uniqueness of a bounded solution under the initial condition are considered in the proposed system. Afterwards, the basic reproduction number R0 is analyzed and it is found to hold a threshold: the disease-free equilibrium point is locally asymptotically stable when R0 ≤ 1, which provides a theoretical basis for whether COVID-19 will become a pandemic in the future.

An improved method to estimate Q based on the logarithmic spectrum of moving peak points

2019 ◽  
Vol 7 (2) ◽  
pp. T255-T263 ◽  
Author(s):  
Yanli Liu ◽  
Zhenchun Li ◽  
Guoquan Yang ◽  
Qiang Liu
Keyword(s):  
Seismic Waves ◽  
Wave Attenuation ◽  
Real Data ◽  
Peak Frequency ◽  
Seismic Reflection Data ◽  
The Real ◽  
Time Frequency ◽  
Reflection Data ◽  
Text Filtering ◽  
The Impact

The quality factor ([Formula: see text]) is an important parameter for measuring the attenuation of seismic waves. Reliable [Formula: see text] estimation and stable inverse [Formula: see text] filtering are expected to improve the resolution of seismic data and deep-layer energy. Many methods of estimating [Formula: see text] are based on an individual wavelet. However, it is difficult to extract the individual wavelet precisely from seismic reflection data. To avoid this problem, we have developed a method of directly estimating [Formula: see text] from reflection data. The core of the methodology is selecting the peak-frequency points to linear fit their logarithmic spectrum and time-frequency product. Then, we calculated [Formula: see text] according to the relationship between [Formula: see text] and the optimized slope. First, to get the peak frequency points at different times, we use the generalized S transform to produce the 2D high-precision time-frequency spectrum. According to the seismic wave attenuation mechanism, the logarithmic spectrum attenuates linearly with the product of frequency and time. Thus, the second step of the method is transforming a 2D spectrum into 1D by variable substitution. In the process of transformation, we only selected the peak frequency points to participate in the fitting process, which can reduce the impact of the interference on the spectrum. Third, we obtain the optimized slope by least-squares fitting. To demonstrate the reliability of our method, we applied it to a constant [Formula: see text] model and the real data of a work area. For the real data, we calculated the [Formula: see text] curve of the seismic trace near a well and we get the high-resolution section by using stable inverse [Formula: see text] filtering. The model and real data indicate that our method is effective and reliable for estimating the [Formula: see text] value.

Comparison of two different types of fractional-order COVID-19 distributed time-delay models with real data application

2021 ◽  
pp. 2150219
Author(s):  
Liangli Yang ◽  
Yongmei Su ◽  
Xinjian Zhuo
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Distributed Delay ◽  
Real Data ◽  
Least Square ◽  
Order Model ◽  
The Real ◽  
Fractional Order Model ◽  
Different Types ◽  
Distributed Time Delay

The outbreak of COVID-19 has a great impact on the world. Considering that there are different infection delays among different populations, which can be expressed as distributed delay, and the distributed time-delay is rarely used in fractional-order model to simulate the real data, here we establish two different types of fractional order (Caputo and Caputo–Fabrizio) COVID-19 models with distributed time-delay. Parameters are estimated by the least-square method according to the report data of China and other 12 countries. The results of Caputo and Caputo–Fabrizio model with distributed time-delay and without delay, the integer-order model with distributed delay are compared. These show that the fractional-order model can be better in fitting the real data. Moreover, Caputo order is better in short-term time fitting, Caputo–Fabrizio order is better in long-term fitting and prediction. Finally, the influence of several parameters is simulated in Caputo order model, which further verifies the importance of taking strict quarantine measures and paying close attention to the incubation period population.

scholarly journals COVID-19 pandemic control using restrictions and vaccination

2021 ◽  
Vol 19 (2) ◽  
pp. 1355-1372
Author(s):  
Vinicius Piccirillo ◽  
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Real Data ◽  
The United States ◽  
Prevention Policy ◽  
Autoregressive Integrated Moving Average ◽  
Infected People ◽  
Marquardt Algorithm ◽  
The Impact ◽  
Methods Numerical

<abstract><p>This work deals with the impact of the vaccination in combination with a restriction parameter that represents non-pharmaceutical interventions measures applied to the compartmental SEIR model in order to control the COVID-19 epidemic. This restriction parameter is used as a control parameter, and the univariate autoregressive integrated moving average (ARIMA) is used to forecast the time series of vaccination of all individuals of a specific country. Having in hand the time series of the population fully vaccinated (real data + forecast), the Levenberg–Marquardt algorithm is used to fit an analytic function that models this evolution over time. Here, it is used two time series of real data that refer to a slow vaccination obtained from India and Brazil, and two faster vaccination as observed in Israel and the United States of America. Together with vaccination, two different control approaches are presented in this paper, which enable reduces the infected people successfully: namely, the feedback and nonfeedback control methods. Numerical results predict that vaccination can reduce the peaks of infections and the duration of the pandemic, however, a better result is achieved when the vaccination is combined with any restrictions or prevention policy.</p></abstract>

scholarly journals Fractional Order Forced Convection Carbon Nanotube Nanofluid Flow Passing Over a Thin Needle

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 312 ◽  
Author(s):  
Taza Gul ◽  
Muhammad Khan ◽  
Waqas Noman ◽  
Ilyas Khan ◽  
Tawfeeq Abdullah Alkanhal ◽  
...  
Keyword(s):  
Carbon Nanotubes ◽  
Forced Convection ◽  
Fractional Order ◽  
Numerical Solutions ◽  
Classical Model ◽  
Single Wall Carbon Nanotubes ◽  
Physical Parameters ◽  
Suitable Model ◽  
Layer Flow ◽  
The Impact

In the fields of fluid dynamics and mechanical engineering, most nanofluids are generally not linear in character, and the fractional order model is the most suitable model for representing such phenomena rather than other traditional approaches. The forced convection fractional order boundary layer flow comprising single-wall carbon nanotubes (SWCNTs) and multiple-wall carbon nanotubes (MWCNTs) with variable wall temperatures passing over a needle was examined. The numerical solutions for the similarity equations were obtained for the integer and fractional values by applying the Adams-type predictor corrector method. A comparison of the SWCNTs and MWCNTs for the classical and fractional schemes was investigated. The classical and fractional order impact of the physical parameters such as skin fraction and Nusselt number are presented physically and numerically. It was observed that the impact of the physical parameters over the momentum and thermal boundary layers in the classical model were limited; however, while utilizing the fractional model, the impact of the parameters varied at different intervals.

Influence of Foundation Pit Excavation on Adjacent Railways and Strengthening Measures

2013 ◽  
Vol 838-841 ◽  
pp. 1256-1262
Author(s):  
Yun Wen Zheng ◽  
Quan Mei Gong ◽  
Yun Zhuang Zheng
Keyword(s):  
Numerical Simulation ◽  
High Pressure ◽  
Real Data ◽  
Vertical Deformation ◽  
Reinforcement Effect ◽  
Foundation Pit ◽  
The Real ◽  
Railway Line ◽  
Jet Grouting ◽  
The Impact

The excavation of foundation pits near existing railway will cause innegligible deformation for the railway line. This paper first conducts numerical simulation for the impact of the excavation of foundation pit for a building close to existing railway lines on the deformation of the railway, and arrives at such conclusions: the excavation of foundation pits has a great impact on the railway lines. The amount of vertical deformation is beyond the requirements of relevant regulations. Accordingly, the foundation needs stabilizing treatment. After the reinforcement of high pressure jet-grouting pile, the maximum vertical deformation decreases obviously to meets the requirements. On this basis, the paper analyzes the reduction amount on different phases of the excavation to work out their respective reinforcement effect. After that, it compares the results with the real data collected during the construction to test the correctness of the model, finds out the major periods during which the vertical deformation occurs as well as the amount of deformation in each period, and points out the worst period for railway deformation during the excavation of foundation pit.

A fractional-order model of HIV infection: Numerical solution and comparisons with data of patients

2014 ◽  
Vol 07 (04) ◽  
pp. 1450036 ◽  
Author(s):  
A. A. M. Arafa ◽  
S. Z. Rida ◽  
M. Khalil
Keyword(s):  
Fractional Order ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Real Data ◽  
Euler Method ◽  
Order Model ◽  
Fractional Order Model ◽  
Plasma Virus Load ◽  
Hiv 1

In this paper, a fractional-order model which describes the human immunodeficiency type-1 virus (HIV-1) infection is presented. Numerical solutions are obtained using a generalized Euler method (GEM) to handle the fractional derivatives. The fractional derivatives are described in the Caputo sense. We show that the model established in this paper possesses non-negative solutions. Comparisons between the results of the fractional-order model, the results of the integer model and the measured real data obtained from 10 patients during primary HIV-1 infection are presented. These comparisons show that the results of the fractional-order model give predictions to the plasma virus load of the patients better than those of the integer model.

scholarly journals A case study of 2019-nCOV cases in Argentina with the real data based on daily cases from March 03, 2020 to March 29, 2021 using classical and fractional derivatives

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Pushpendra Kumar ◽  
Vedat Suat Erturk ◽  
Marina Murillo-Arcila ◽  
Ramashis Banerjee ◽  
A. Manickam
Keyword(s):  
Fractional Order ◽  
Trust Region ◽  
Simulated Data ◽  
Real Data ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Order Model ◽  
The Real ◽  
The Stability ◽  
Parameter Values

AbstractIn this study, our aim is to explore the dynamics of COVID-19 or 2019-nCOV in Argentina considering the parameter values based on the real data of this virus from March 03, 2020 to March 29, 2021 which is a data range of more than one complete year. We propose a Atangana–Baleanu type fractional-order model and simulate it by using predictor–corrector (P-C) method. First we introduce the biological nature of this virus in theoretical way and then formulate a mathematical model to define its dynamics. We use a well-known effective optimization scheme based on the renowned trust-region-reflective (TRR) method to perform the model calibration. We have plotted the real cases of COVID-19 and compared our integer-order model with the simulated data along with the calculation of basic reproductive number. Concerning fractional-order simulations, first we prove the existence and uniqueness of solution and then write the solution along with the stability of the given P-C method. A number of graphs at various fractional-order values are simulated to predict the future dynamics of the virus in Argentina which is the main contribution of this paper.

scholarly journals A new regression model for bounded response variable: An alternative to the beta and unit-Lindley regression models

PLoS ONE ◽  
2021 ◽  
Vol 16 (1) ◽  
pp. e0245627
Author(s):  
Emrah Altun ◽  
M. El-Morshedy ◽  
M. S. Eliwa
Keyword(s):  
Parameter Estimation ◽  
Regression Model ◽  
Regression Models ◽  
Real Data ◽  
Quantile Function ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Response Variable ◽  
Parameter Estimation Methods

A new distribution defined on (0,1) interval is introduced. Its probability density and cumulative distribution functions have simple forms. Thanks to its simple forms, the moments, incomplete moments and quantile function of the proposed distribution are derived and obtained in explicit forms. Four parameter estimation methods are used to estimate the unknown parameter of the distribution. Besides, simulation study is implemented to compare the efficiencies of these parameter estimation methods. More importantly, owing to the proposed distribution, we provide an alternative regression model for the bounded response variable. The proposed regression model is compared with the beta and unit-Lindley regression models based on two real data sets.

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