ABSTRACT
Apart from the many social and health problems it has caused, the COVID-19 pandemic has had a severe impact on most sectors of the economy worldwide. One of the areas where such impact is noticeable is the textile, apparel, and fashion (TAF) industry. The lockdowns and limited access to retailer outlets resulted in a considerable drop in consumption, creating problems related to the excess of stock, the decrease of sales, and the disposal of non-used items. This paper outlines the implications of the COVID-19 on the TAF sectors and European retailers. It analyzes how the current supply chains exacerbated stock control problems, and it reports on the changes in consumption during the pandemic. The worldwide restrictive measures implemented to cope with the COVID-19 pandemic were responsible for significant profit losses. Also, the decrease in consumption, caused by several geographically wide lockdowns, prompted a subsequent reduction in orders and sales, resulting in a significant number of constraints. The implementation of more environmentally friendly processes, including sustainable circularity as a competitiveness source to keep the TAF sectors in the loop and reduce greenhouse gas emissions, may help address the problems associated with the COVID-19 pandemic in the sustainability context, as reported in this paper. © The Author(s) 2022.
ABSTRACT
Apart from the many social and health problems it has caused, the COVID-19 pandemic has had a severe impact on most sectors of the economy worldwide. One of the areas where such impact is noticeable is the textile, apparel, and fashion (TAF) industry. The lockdowns and limited access to retailer outlets resulted in a considerable drop in consumption, creating problems related to the excess of stock, the decrease of sales, and the disposal of non-used items. This paper outlines the implications of the COVID-19 on the TAF sectors and European retailers. It analyzes how the current supply chains exacerbated stock control problems, and it reports on the changes in consumption during the pandemic. The worldwide restrictive measures implemented to cope with the COVID-19 pandemic were responsible for significant profit losses. Also, the decrease in consumption, caused by several geographically wide lockdowns, prompted a subsequent reduction in orders and sales, resulting in a significant number of constraints. The implementation of more environmentally friendly processes, including sustainable circularity as a competitiveness source to keep the TAF sectors in the loop and reduce greenhouse gas emissions, may help address the problems associated with the COVID-19 pandemic in the sustainability context, as reported in this paper. © The Author(s) 2022.
ABSTRACT
A novel coronavirus is a serious global issue and has a negative impact on the economy of Egypt. According to the publicly reported data, the first case of the novel corona virus in Egypt was reported on 14 February 2020. Total of 96753 cases were recorded in Egypt from the beginning of the pandemic until the eighteenth of August, where 96, 581 individuals were Egyptians and 172 were foreigners. Recently, many mathematical models have been considered to better understand coronavirus infection. Most of these models are based on classical integer-order derivatives which can not capture the fading memory and crossover behavior found in many biological phenomena. Therefore, we study the coronavirus disease in this paper by exploring the dynamics of COVID-19 infection using new variable-order fractional derivatives. This paper presents an optimal control problem of the hybrid variable-order fractional model of Coronavirus. The variable-order fractional operator is modified by an auxiliary parameter in order to satisfy the dimensional matching between the both sides of the resultant variable-order fractional equations. Existence, uniqueness, boundedness, positivity, local and global stability of the solutions are proved. Two control variables are considered to reduce the transmission of infection into healthy people. To approximate the new hybrid variable-order operator, Grünwald-Letnikov approximation is used. Finite difference method with a hybrid variable-order operator and generalized fourth order Runge-Kutta method are used to solve the optimality system. Numerical examples and comparative studies for testing the applicability of the utilized methods and to show the simplicity of these approximation approaches are presented. Moreover, by using the proposed methods we can concluded that, the model given in this paper describes well the confirmed real data given by WHO about Egypt.
ABSTRACT
In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald-Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.
ABSTRACT
Introduction: Coronavirus COVID-19 pandemic is the defining global health crisis of our time and the greatest challenge we have faced since world war two. To describe this disease mathematically, we noted that COVID-19, due to uncertainties associated to the pandemic, ordinal derivatives and their associated integral operators show deficient. The fractional order differential equations models seem more consistent with this disease than the integer order models. This is due to the fact that fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes. Hence there is a growing need to study and use the fractional order differential equations. Also, optimal control theory is very important topic to control the variables in mathematical models of infectious disease. Moreover, a hybrid fractional operator which may be expressed as a linear combination of the Caputo fractional derivative and the Riemann-Liouville fractional integral is recently introduced. This new operator is more general than the operator of Caputo's fractional derivative. Numerical techniques are very important tool in this area of research because most fractional order problems do not have exact analytic solutions. Objectives: A novel fractional order Coronavirus (2019-nCov) mathematical model with modified parameters will be presented. Optimal control of the suggested model is the main objective of this work. Three control variables are presented in this model to minimize the number of infected populations. Necessary control conditions will be derived. Methods: The numerical methods used to study the fractional optimality system are the weighted average nonstandard finite difference method and the Grünwald-Letnikov nonstandard finite difference method. Results: The proposed model with a new fractional operator is presented. We have successfully applied a kind of Pontryagin's maximum principle and were able to reduce the number of infected people using the proposed numerical methods. The weighted average nonstandard finite difference method with the new operator derivative has the best results than Grünwald-Letnikov nonstandard finite difference method with the same operator. Moreover, the proposed methods with the new operator have the best results than the proposed methods with Caputo operator. Conclusions: The combination of fractional order derivative and optimal control in the Coronavirus (2019-nCov) mathematical model improves the dynamics of the model. The new operator is more general and suitable to study the optimal control of the proposed model than the Caputo operator and could be more useful for the researchers and scientists.