scholarly journals Modeling the Evolution of SARS-CoV-2 Using a Fractional-Order SIR Approach

TecnoLógicas ◽  
2021 ◽  
Vol 24 (51) ◽  
pp. e1866
Author(s):  
Anderson S. Quintero ◽  
Ricardo E. Gutiérrez-Carvajal
Keyword(s):  
Fractional Order ◽  
Maximum Error ◽  
Optimization Method ◽  
Transformation Method ◽  
Sir Model ◽  
Model Parameters ◽  
Population Distributions ◽  
Substantial Change ◽  
Error Percentage ◽  
Bound Optimization

To show the potential of non-commensurable fractional-order dynamical systems in modeling epidemiological phenomena, we will adjust the parameters of a fractional generalization of the SIR model to describe the population distributions generated by SARS-CoV-2 in France and Colombia. Despite the completely different contexts of both countries, we will see how the system presented here manages to adequately model them thanks to the flexibility provided by the fractional-order differential equations. The data for Colombia were obtained from the records published by the Colombian Ministry of Information Technology and Communications from March 24 to July 10, 2020. Those for France were taken from the information published by the Ministry of Solidarity and Health from May 1 to September 6, 2020. As for the methodology implemented in this study, we conducted an exploratory analysis focused on solving the fractional SIR model by means of the fractional transformation method. In addition, the model parameters were adjusted using a sophisticated optimization method known as the Bound Optimization BY Quadratic Approximation (BOBYQA) algorithm. According to the results, the maximum error percentage for the evolution of the susceptible, infected, and recovered populations in France was 0.05%, 19%, and 6%, respectively, while that for the evolution of the susceptible, infected, and recovered populations in Colombia was 0.003%, 19%, and 38%, respectively. This was considered for data in which the disease began to spread and human intervention did not imply a substantial change in the community.

scholarly journals Optimal solution of the fractional order breast cancer competition model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
H. Hassani ◽  
J. A. Tenreiro Machado ◽  
Z. Avazzadeh ◽  
E. Safari ◽  
S. Mehrabi
Keyword(s):  
Breast Cancer ◽  
Fractional Order ◽  
Legendre Polynomials ◽  
Numerical Experiments ◽  
Optimal Solution ◽  
Optimization Method ◽  
Competition Model ◽  
Basis Functions ◽  
Cell Populations ◽  
Operational Matrices

AbstractIn this article, a fractional order breast cancer competition model (F-BCCM) under the Caputo fractional derivative is analyzed. A new set of basis functions, namely the generalized shifted Legendre polynomials, is proposed to deal with the solutions of F-BCCM. The F-BCCM describes the dynamics involving a variety of cancer factors, such as the stem, tumor and healthy cells, as well as the effects of excess estrogen and the body’s natural immune response on the cell populations. After combining the operational matrices with the Lagrange multipliers technique we obtain an optimization method for solving the F-BCCM whose convergence is investigated. Several examples show that a few number of basis functions lead to the satisfactory results. In fact, numerical experiments not only confirm the accuracy but also the practicability and computational efficiency of the devised technique.

scholarly journals Adaptive State-of-Charge Estimation for Lithium-Ion Batteries by Considering Capacity Degradation

Electronics ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 122
Author(s):  
Peipei Xu ◽  
Junqiu Li ◽  
Chao Sun ◽  
Guodong Yang ◽  
Fengchun Sun
Keyword(s):  
Equivalent Circuit Model ◽  
Lithium Ion ◽  
Maximum Error ◽  
State Of Charge ◽  
Recursive Least Squares ◽  
Accurate Estimation ◽  
Model Parameters ◽  
Soc Estimation ◽  
Capacity Degradation ◽  
Battery Capacity

The accurate estimation of a lithium-ion battery’s state of charge (SOC) plays an important role in the operational safety and driving mileage improvement of electrical vehicles (EVs). The Adaptive Extended Kalman filter (AEKF) estimator is commonly used to estimate SOC; however, this method relies on the precise estimation of the battery’s model parameters and capacity. Furthermore, the actual capacity and battery parameters change in real time with the aging of the batteries. Therefore, to eliminate the influence of above-mentioned factors on SOC estimation, the main contributions of this paper are as follows: (1) the equivalent circuit model (ECM) is presented, and the parameter identification of ECM is performed by using the forgetting-factor recursive-least-squares (FFRLS) method; (2) the sensitivity of battery SOC estimation to capacity degradation is analyzed to prove the importance of considering capacity degradation in SOC estimation; and (3) the capacity degradation model is proposed to perform the battery capacity prediction online. Furthermore, an online adaptive SOC estimator based on capacity degradation is proposed to improve the robustness of the AEKF algorithm. Experimental results show that the maximum error of SOC estimation is less than 1.3%.

scholarly journals Modelling the spread of American foulbrood in honeybees

2013 ◽  
Vol 10 (88) ◽  
pp. 20130650 ◽  
Author(s):  
Samik Datta ◽  
James C. Bull ◽  
Giles E. Budge ◽  
Matt J. Keeling
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Control Strategies ◽  
Sir Model ◽  
Model Parameters ◽  
American Foulbrood ◽  
Inspection Period ◽  
Stochastic Sir ◽  
Stochastic Sir Model ◽  
The Impact

We investigate the spread of American foulbrood (AFB), a disease caused by the bacterium Paenibacillus larvae , that affects bees and can be extremely damaging to beehives. Our dataset comes from an inspection period carried out during an AFB epidemic of honeybee colonies on the island of Jersey during the summer of 2010. The data include the number of hives of honeybees, location and owner of honeybee apiaries across the island. We use a spatial SIR model with an underlying owner network to simulate the epidemic and characterize the epidemic using a Markov chain Monte Carlo (MCMC) scheme to determine model parameters and infection times (including undetected ‘occult’ infections). Likely methods of infection spread can be inferred from the analysis, with both distance- and owner-based transmissions being found to contribute to the spread of AFB. The results of the MCMC are corroborated by simulating the epidemic using a stochastic SIR model, resulting in aggregate levels of infection that are comparable to the data. We use this stochastic SIR model to simulate the impact of different control strategies on controlling the epidemic. It is found that earlier inspections result in smaller epidemics and a higher likelihood of AFB extinction.

Closed Loop Identification by Optimization Method

2015 ◽  
Vol 1084 ◽  
pp. 636-641
Author(s):  
Valeriy F. Dyadik ◽  
Nikolay S. Krinitsyn ◽  
Vyacheslav A. Rudnev
Keyword(s):  
Closed Loop ◽  
Uranium Hexafluoride ◽  
Optimization Method ◽  
Model Parameters ◽  
Control Loop ◽  
Loop Control ◽  
Identification Method ◽  
Closed Loop Control System ◽  
Closed Loop Identification ◽  
Loop Control System

The article is devoted to the adaptation of the controller parameters during its operation as a part of a control loop. The possibility to identify the parameters of the controlled plant model in the closed control loop has been proved by a computer simulation. The described active identification method is based on the response processing of the closed loop control system to standard actions. The developed algorithm has been applied to determine the model parameters of the flaming fluorination reactor used for the production of uranium hexafluoride. Designed identification method improves the quality of the product and the efficiency of the entire production.

scholarly journals LWD DATA INVERSION FOR STRUCTURE WITH ANGULAR UNCONFORMITY

2021 ◽  
Vol 2 (1) ◽  
pp. 336-344
Author(s):  
Anna S. Astrakova ◽  
Elena V. Konobriy ◽  
Dmitry Yu. Kushnir ◽  
Nikolay N. Velker ◽  
Gleb V. Dyatlov
Keyword(s):  
Real Time ◽  
Optimization Method ◽  
Parametric Model ◽  
Model Parameters ◽  
Time Inversion ◽  
Water Contact ◽  
2D Inversion ◽  
Angular Unconformity ◽  
Oil Water ◽  
2D Resistivity

Non-structural traps and reservoir flanks are characterized by angular unconformities. Angular unconformity between dipping formation and sub-horizontal oil-water contact is common in the North Sea fields. This paper presents an approach to real-time inversion of LWD resistivity data for the scenario with angular unconformity. The approach utilizes artificial neural networks (ANNs) for calculating the tool responses in parametric surface-based 2D resistivity models. We propose a parametric model with two non-parallel boundaries suitable for scenarios with angular unconformity and pinch-out. Training of ANNs for this parametric model is performed using a database containing samples with the model parameters and corresponding tool responses. ANNs are the kernel of 2D inversion based on the Levenberg-Marquardt optimization method. To demonstrate applicability of our approach and compare with the results of 1D inversion, we analyze Extra Deep Azimuthal Resistivity tool responses in a 2D synthetic model. It is shown that 1D inversion determines either the position of the oil-water contact or dipping layers structure. At the same time, 2D inversion makes it possible to correctly reconstruct the positions of non-parallel boundaries. Performance of 2D inversion based on ANNs is suitable for real-time applications.

scholarly journals A Modified Techniques of Fractional-Order Cauchy-Reaction Diffusion Equation via Shehu Transform

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Mounirah Areshi ◽  
A. M. Zidan ◽  
Rasool Shah ◽  
Kamsing Nonlaopon
Keyword(s):  
Fractional Order ◽  
Reaction Diffusion ◽  
Approximate Solutions ◽  
Transformation Method ◽  
Reaction Diffusion Equations ◽  
Reaction Diffusion Equation ◽  
Closed Form Solutions ◽  
Homotopy Perturbation ◽  
In Series ◽  
The Given

In this article, the iterative transformation method and homotopy perturbation transformation method are applied to calculate the solution of time-fractional Cauchy-reaction diffusion equations. In this technique, Shehu transformation is combined of the iteration and the homotopy perturbation techniques. Four examples are examined to show validation and the efficacy of the present methods. The approximate solutions achieved by the suggested methods indicate that the approach is easy to apply to the given problems. Moreover, the solution in series form has the desire rate of convergence and provides closed-form solutions. It is noted that the procedure can be modified in other directions of fractional order problems. These solutions show that the current technique is very straightforward and helpful to perform in applied sciences.

scholarly journals Solutions of Conformable Fractional-Order SIR Epidemic Model

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Atimad Harir ◽  
Said Malliani ◽  
Lalla Saadia Chandli
Keyword(s):  
Fractional Order ◽  
Epidemic Model ◽  
Analytic Solution ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Transformation Method ◽  
Conformable Fractional Derivative ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Fractional Differential

In this paper, the conformable fractional-order SIR epidemic model are solved by means of an analytic technique for nonlinear problems, namely, the conformable fractional differential transformation method (CFDTM) and variational iteration method (VIM). These models are nonlinear system of conformable fractional differential equation (CFDE) that has no analytic solution. The VIM is based on conformable fractional derivative and proved. The result revealed that both methods are in agreement and are accurate and efficient for solving systems of OFDE.

scholarly journals Prediction of peak and termination of novel coronavirus COVID-19 epidemic in Iran

2020 ◽  
Vol 31 (11) ◽  
pp. 2050152
Author(s):  
Sepehr Rafieenasab ◽  
Amir-Pouyan Zahiri ◽  
Ehsan Roohi
Keyword(s):  
Statistical Data ◽  
Sir Model ◽  
Model Parameters ◽  
Peak Time ◽  
Infected People ◽  
Epidemic Curve ◽  
Immunization Rates ◽  
Long Time ◽  
Novel Coronavirus ◽  
Official Data

The growth and development of COVID-19 transmission have significantly attracted the attention of many societies, particularly Iran, that have been struggling with this contagious, infectious disease since late February 2020. In this study, the known “Susceptible-Infectious-Recovered (SIR)” and some other mathematical approaches were used to investigate the dynamics of the COVID-19 epidemic to provide a suitable assessment of the COVID-19 virus epidemic in Iran. The epidemic curve and SIR model parameters were obtained with the use of Iran’s official data. The recovered people were considered alongside the official number of confirmed victims as the reliable long-time statistical data. The results offer important predictions of the COVID-19 virus epidemic such as the realistic number of victims, infection rate, peak time and other characteristics. Besides, the effectiveness of infection and immunization rates to the number of infected people and epidemic end time are reported. Finally, different suggestions for decreasing victims are offered.

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