scholarly journals CAPUTO TYPE FRACTIONAL OPERATOR APPLIED TO HEPATITIS B SYSTEM

Fractals ◽  
2021 ◽  
pp. 2240023 ◽  
Author(s):  
ANWARUD DIN ◽  
YONGJIN LI ◽  
ABDULLAHI YUSUF ◽  
ALIYU ISA ALI

In our research work, we develop the analysis of a noninteger-order model for hepatitis B (HBV) under singular type Caputo fractional-order derivative. We investigated our proposed system for an approximate or semi-analytical solution using Laplace transform along with decomposition techniques by Adomian polynomial of nonlinear terms and some perturbation techniques of Homotopy (HPM). The obtained solutions have been compared with each other against some real data by simulation via MATLAB. The graphical simulation in fractional form shows a better general result as compared to integer-order simulation.

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Weiqiu Pan ◽  
Tianzeng Li ◽  
Safdar Ali

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.


Author(s):  
Liangli Yang ◽  
Yongmei Su ◽  
Xinjian Zhuo

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.


2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhengyou Xia ◽  
Shengwu Xu ◽  
Ningzhong Liu ◽  
Zhengkang Zhao

The most current news recommendations are suitable for news which comes from a single news website, not for news from different heterogeneous news websites. Previous researches about news recommender systems based on different strategies have been proposed to provide news personalization services for online news readers. However, little research work has been reported on utilizing hundreds of heterogeneous news websites to provide top hot news services for group customers (e.g., government staffs). In this paper, we propose a hot news recommendation model based on Bayesian model, which is from hundreds of different news websites. In the model, we determine whether the news is hot news by calculating the joint probability of the news. We evaluate and compare our proposed recommendation model with the results of human experts on the real data sets. Experimental results demonstrate the reliability and effectiveness of our method. We also implement this model in hot news recommendation system of Hangzhou city government in year 2013, which achieves very good results.


Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Ruiqing Shi ◽  
Ting Lu ◽  
Cuihong Wang

In this paper, a fractional-order model is constructed to describe the transmission of Hepatitis B Virus (HBV). Firstly, the existence and uniqueness of positive solutions are proved. Secondly, the basic reproduction number and the sufficient conditions for the existence of two equilibriums are obtained. Thirdly, the stability of equilibriums are analyzed. After that, some numerical simulations are performed to verify the theoretical prediction. Finally, a brief discussion is presented.


2020 ◽  
Vol 538 ◽  
pp. 122636 ◽  
Author(s):  
Syed Azhar Ali Shah ◽  
Muhammad Altaf Khan ◽  
Muhammad Farooq ◽  
Saif Ullah ◽  
Ebraheem O. Alzahrani

Energies ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 2899
Author(s):  
Abhinandana Boodi ◽  
Karim Beddiar ◽  
Yassine Amirat ◽  
Mohamed Benbouzid

This paper proposes an approach to develop building dynamic thermal models that are of paramount importance for controller application. In this context, controller requires a low-order, computationally efficient, and accurate models to achieve higher performance. An efficient building model is developed by having proper structural knowledge of low-order model and identifying its parameter values. Simplified low-order systems can be developed using thermal network models using thermal resistances and capacitances. In order to determine the low-order model parameter values, a specific approach is proposed using a stochastic particle swarm optimization. This method provides a significant approximation of the parameters when compared to the reference model whilst allowing low-order model to achieve 40% to 50% computational efficiency than the reference one. Additionally, extensive simulations are carried to evaluate the proposed simplified model with solar radiation and identified model parameters. The developed simplified model is afterward validated with real data from a case study building where the achieved results clearly show a high degree of accuracy compared to the actual data.


2020 ◽  
Vol 21 (1) ◽  
pp. 27
Author(s):  
Maria Christina Prihatiningsih ◽  
Sri Sundari Retnoasih ◽  
Athanasia Elra Andjioe ◽  
Noor Anis Kundari ◽  
Edy Giri Rachman Putra

In order to investigate the potential of Al_SBA-16 Mesoporous Nanomaterial as a candidate for radiopharmaceutical vehicles, the studies of kinetics, thermodynamic, and in vitro stability of Iodide adsorption onto the nanomaterial have been carried out. The adsorption study was conducted at different temperature, time, and iodide concentration and observed with spectrophotometric techniques. The isotherm adsorption was fitted with Langmuir and Freundlich model and the thermodynamic parameters were determined at temperatures of 293K, 301K, 308K, and 313K. Moreover, the adsorption kinetics was analyzed in terms of pseudo first order model for Al_SBA-16 Mesoporous Nanomaterial and Iodide and pseudo second order in overall reaction. The activation energy was determined by using Arrhenius equation, meanwhile, the in vitro stability testing was conducted in phosphate buffer saline at pH variation for 5.5 to 7.0, and at temperature variation for 20C to 45C and at testing time variation for 6 to 48 hours. The result indicate that the adsorption obeys the Langmuir isotherm model and has a tendency to be chemical adsorption with a value of H was -116.641 kJ/mol and the nature of spontaneous reactions. The adsorption process followed the pseudo-first-order model and the apparent activation energy was 41.26 kJ/mol. In the present research work, the in vitro stability data were evaluated using P-Value and the theory of Hypothesis Testing or Fisher's significance test. The result of hypothesis testing show that, the adsorption of iodide onto Al_SBA-16 Mesoporous Nanomaterial were highly stable under the experimental conditions adopted.


Author(s):  
Paula Rodríguez-Abruñeiras ◽  
Jesús Romero-Barranco

The present paper deals with a proposal for enhancing students’ engagement in the course ‘History of the English Language’ of the Degree in English Studies (Universitat de València). For the purpose, the traditional lectures will be combined with a research project carried out by groups of students (research teams) in which two digital tools will be used: electronic linguistic corpora and YouTube. Electronic linguistic corpora, on the one hand, will allow students to discover the diachronic development of certain linguistic features by looking at real data and making conclusions based on frequencies by themselves. YouTube, on the other, is a most appropriate online environment where students will share a video lecture so that their classmates can benefit from the research work they did, fostering peer-to-peer learning. The expected results are to make students more autonomous in their learning process, as they will be working on their project from the very beginning of the course; and to engage them more effectively since they will be working in a format that resembles what they do at their leisure time.


2019 ◽  
pp. 455-461
Author(s):  
Yuliya Vystavna

Water quantity and quality are important aspects of water management concerning to thepollution control as economic and environmental safety of any countries, Due to intensiveexploitation and inadequate pollution control Ukraine faces with degradation of natural waterresources. The Kharkiv region is an industrially developed region of Ukraine with highpopulation density and water resources scarcity, The disproportion in economical and waterresource potentials of the region and significant anthropogenic loadings on the water sourceslead to depletion and pollution of ones, and, as a consequence, to the water deficiency,Dwelling sector and office buildings are one of the most powerful water consumers onurbanized territories, Every day the big Ukrainian city, like Kharkiv, consumes no less than200 million of cub,m water per year and 80 % of that for households water supplying, Thepowerful water consumption leads to the degradation of water resource, especially, in the bigcities with water scarcity,The aim of the work is to find a new optimal level of water resource consumption forhouseholds and office buildings on urbanized territory to base on environmental, economicand social aspects of water use, An environmental engineering modelling, risk assessment andeconomic methods of analysis have been used for the research work,The balanced model of quality of water environment and public water demand weredeveloped by real data, The regression parameters were determined for such indicators ofwater quality as suspended solids, mineralization, ammonium, nitrites, chlorides,Using the model it is possible to analyze environmental impacts of municipal waterconsumption and find the optimal level of public water supply,Also the environmental, economic and social criteria of water saving were developed,


2019 ◽  
Vol 16 (8) ◽  
pp. 3219-3221
Author(s):  
A. Viji Amutha Mary

All our day’s work in this world of science is done with useful data. These useful data or information is extracted from raw facts. From the information, knowledge is gained. This knowledge is used by the customers for beneficial outcome. Here comes the concept of data mining. An important query arises as how to preserve these data. This concept is called as Privacy Preserving with Data Mining (PPDM). Many PPDM techniques are available to protect the data. The PPDM technique is useful in fields like medicine, forensics, defence, etc to preserve the confidential data. The existing techniques protect the secret data either by perturbing or by hiding them. Moreover, most of the techniques focus only on the numerical data. Very few perturbation techniques like translation, multiplicative and rotation perturb the images. But these techniques are very easily attacked by third parties since the transformation is a linear one. The Research Work aims to overcome the drawbacks of the existing perturbation techniques. The main objective of the Research Work is to improve the privacy level of the images by implementing a Random Projection (RP) technique. The remarkable features and benefits of the RP technique are pinpointed.


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