Numerical Simulation for COVID-19 Model Using a Multidomain Spectral Relaxation Technique

The major objective of this work is to evaluate and study the model of coronavirus illness by providing an efficient numerical solution for this important model. The model under investigation is composed of five differential equations. In this study, the multidomain spectral relaxation method (MSRM) is used to numerically solve the suggested model. The proposed approach is based on the hypothesis that the domain of the problem can be split into a finite number of subintervals, each of which can have a solution. The procedure also converts the proposed model into a system of algebraic equations. Some theoretical studies are provided to discuss the convergence analysis of the suggested scheme and deduce an upper bound of the error. A numerical simulation is used to evaluate the approach's accuracy and utility, and it is presented in symmetric forms.

A study on fractional COVID-19 disease model by using Hermite wavelets.

The preeminent target of present study is to reveal the speed characteristic of ongoing outbreak COVID-19 due to novel coronavirus. On January 2020, the novel coronavirus infection (COVID-19) detected in India, and the total statistic of cases continuously increased to 7 128 268 cases including 109 285 deceases to October 2020, where 860 601 cases are active in India. In this study, we use the Hermite wavelets basis in order to solve the COVID-19 model with time- arbitrary Caputo derivative. The discussed framework is based upon Hermite wavelets. The operational matrix incorporated with the collocation scheme is used in order to transform arbitrary-order problem into algebraic equations. The corrector scheme is also used for solving the COVID-19 model for distinct value of arbitrary order. Also, authors have investigated the various behaviors of the arbitrary-order COVID-19 system and procured developments are matched with exiting developments by various techniques. The various illustrations of susceptible, exposed, infected, and recovered individuals are given for its behaviors at the various value of fractional order. In addition, the proposed model has been also supported by some numerical simulations and wavelet-based results.

Russian gas in Europe: pipeline and hubs price convergence analysis

The analysis in this paper was performed before the disastrous and unsolicited invasion of Russia to Ukraine. The paper aims to identify if the biggest Russian gas exporter Gazprom used market power to decouple its gas prices from European gas hub benchmarks. The empirical analysis is based on pairwise price convergence between the Russian pipeline and European gas hubs. The main finding shows that Gazprom takes advantage of its market position. The proposed model does not support the company's claims of pipeline price tightness to liquid European gas hubs, and rather proves fluctuating and unstable price convergence between pipelines and hubs from 2016 to March 2020, right before the COVID-19 pandemic. Notably, a robust and trendy-stable price convergence is observed between the Russian pipeline gas and Brent benchmark. Methodologically, the paper contributes with a modified convergence model compliant with gas market fundamentals and suggests a time-expanding concept missed in previous studies. Ongoing political and European gas market developments of 2022 (during the paper review) support the conclusions. © 2022 Taylor & Francis Group, LLC.

An efficient nonstandard computer method to solve a compartmental epidemiological model for COVID-19 with vaccination and population migration.

BACKGROUND AND OBJECTIVE: In this manuscript, we consider a compartmental model to describe the dynamics of propagation of an infectious disease in a human population. The population considers the presence of susceptible, exposed, asymptomatic and symptomatic infected, quarantined, recovered and vaccinated individuals. In turn, the mathematical model considers various mechanisms of interaction between the sub-populations in addition to population migration. METHODS: The steady-state solutions for the disease-free and endemic scenarios are calculated, and the local stability of the equilibium solutions is determined using linear analysis, Descartes' rule of signs and the Routh-Hurwitz criterion. We demonstrate rigorously the existence and uniqueness of non-negative solutions for the mathematical model, and we prove that the system has no periodic solutions using Dulac's criterion. To solve this system, a nonstandard finite-difference method is proposed. RESULTS: As the main results, we show that the computer method presented in this work is uniquely solvable, and that it preserves the non-negativity of initial approximations. Moreover, the steady-state solutions of the continuous model are also constant solutions of the numerical scheme, and the stability properties of those solutions are likewise preserved in the discrete scenario. Furthermore, we establish the consistency of the scheme and, using a discrete form of Gronwall's inequality, we prove theoretically the stability and the convergence properties of the scheme. For convenience, a Matlab program of our method is provided in the appendix. CONCLUSIONS: The computer method presented in this work is a nonstandard scheme with multiple dynamical and numerical properties. Most of those properties are thoroughly confirmed using computer simulations. Its easy implementation make this numerical approach a useful tool in the investigation on the propagation of infectious diseases. From the theoretical point of view, the present work is one of the few papers in which a nonstandard scheme is fully and rigorously analyzed not only for the dynamical properties, but also for consistently, stability and convergence.

Testing the Club Convergence Dynamics of the COVID-19 Vaccination Rates Across the OECD Countries.

Vaccines are essential to create a more resilient economic growth model. Ending the COVID-19 pandemic requires a more coordinated, effective, and equitable distribution of vaccines across the countries. Therefore, governments are in a race to increase the vaccination rates of the population. Given this backdrop, this paper focuses on the daily vaccinations per million data from March 1, 2021, to October 15, 2021, in 37 Organization for Economic Co-operation and Development (OECD) countries and examines the stochastic properties of the vaccination rates. We adopt the club convergence econometric methodology to investigate the club convergence paths of COVID-19 vaccination rates in OECD regions. The results indicate a significant convergence of the vaccination rates in seven clubs across 30 OECD countries. Moreover, there are seven OECD countries demonstrate non-convergent characteristics, which raises questions about ineffective vaccine balance. In addition, the paper also discusses the potential implications for the post-COVID-19 era.

Construction and numerical analysis of a fuzzy non-standard computational method for the solution of an SEIQR model of COVID-19 dynamics

This current work presents an SEIQR model with fuzzy parameters. The use of fuzzy theory helps us to solve the problems of quantifying uncertainty in the mathematical modeling of diseases. The fuzzy reproduction number and fuzzy equilibrium points have been derived focusing on a model in a specific group of people having a triangular membership function. Moreover, a fuzzy non-standard finite difference (FNSFD) method for the model is developed. The stability of the proposed method is discussed in a fuzzy sense. A numerical verification for the proposed model is presented. The developed FNSFD scheme is a reliable method and preserves all the essential features of a continuous dynamical system.

Numerical Solutions of Fractional Covid-19 Model Using Spectral Collocation Method

In this work, the mathematical model is considered on COVID-19 which makes the lives of people in the world into a hell. This present model has four components that are expressed as susceptible, exposed, infected and recovered (SEIR). Spectral collocation method (SCM) is presented here for numerical simulations because it is one of the important numerical technique having high rate convergence. Also, convergence analysis of the above method is presented here briefly. There is detailed description about the comparision of the rate of increasing of COVID-19 of India, Srilanka, Pakistan, Bangladesh respectively. If the four components are considered as zero initially, the effect of population to increase the disease is presented here. © 2021, Thammasat University. All rights reserved.

Structure preserving algorithm for fractional order mathematical model of COVID-19

In this article, a brief biological structure and some basic properties of COVID-19 are described. A classical integer order model is modified and converted into a fractional order model with ξ as order of the fractional derivative. Moreover, a valued structure preserving the numerical design, coined as Grunwald–Letnikov non-standard finite difference scheme, is developed for the fractional COVID-19 model. Taking into account the importance of the positivity and boundedness of the state variables, some productive results have been proved to ensure these essential features. Stability of the model at a corona free and a corona existing equilibrium points is investigated on the basis of Eigen values. The Routh–Hurwitz criterion is applied for the local stability analysis. An appropriate example with fitted and estimated set of parametric values is presented for the simulations. Graphical solutions are displayed for the chosen values of ξ (fractional order of the derivatives). The role of quarantined policy is also determined gradually to highlight its significance and relevancy in controlling infectious diseases. In the end, outcomes of the study are presented. © 2022 Tech Science Press. All rights reserved.

The role of pre-pandemic teleworking and E-commerce culture in the COVID-19 dispersion in Europe.

The threats of the coronavirus have shifted the workplace of many people from office to home and also made e-commerce the primary medium for purchases. While these changes were made in an effort to mitigate contagion, there are no studies, to the best of our knowledge, that address if teleworking and e-commerce culture prior to the pandemic influenced the dispersion of the virus. In our study we examine whether pre-existing teleworking practices and e-commerce activity have played an important role in the COVID-19 dispersion in Europe. Based on a set of data from all European countries, the present study employs the Philips & Sul methodology to explore corona convergence patterns. Our findings suggest that pre-existing e-commerce activity and teleworking practices had little to no effect in reducing the initial opportunities of individuals to contract the virus leading to the conclusion that other social interactions must have played a more important role.

Design of nonstandard computational method for stochastic susceptible-infected-treated-recovered dynamics of coronavirus model.

The current effort is devoted to investigating and exploring the stochastic nonlinear mathematical pandemic model to describe the dynamics of the novel coronavirus. The model adopts the form of a nonlinear stochastic susceptible-infected-treated-recovered system, and we investigate the stochastic reproduction dynamics, both analytically and numerically. We applied different standard and nonstandard computational numerical methods for the solution of the stochastic system. The design of a nonstandard computation method for the stochastic system is innovative. Unfortunately, standard computation numerical methods are time-dependent and violate the structure properties of models, such as positivity, boundedness, and dynamical consistency of the stochastic system. To that end, convergence analysis of nonstandard computational methods and simulation with a comparison of standard computational methods are presented.