The Analytic Solutions of the Fractional-Order Model for the Spatial Epidemiology of the COVID-19 Infection

This paper provides a mathematical fractional-order model that accounts for the mindset of patients in the transmission of COVID-19 disease, the continuous inflow of foreigners into the country, immunization of population subjects, and temporary loss of immunity by recovered individuals. The analytic solutions, which are given as series solutions, are derived using the fractional power series method (FPSM) and the residual power series method (RPSM). In comparison, the series solution for the number of susceptible members, using the FPSM, is proportional to the series solution, using the RPSM for the first two terms, with a proportional constant of ψΓnα+1, where ψ is the natural birth rate of the baby into the susceptible population, Γ is the gamma function, n is the nth term of the series, and α is the fractional order as the initial number of susceptible individuals approaches the population size of Ghana. However, the variation in the two series solutions of the number of members who are susceptible to the COVID-19 disease begins at the third term and continues through the remaining terms. This is brought on by the nonlinear function present in the equation for the susceptible subgroup. The similar finding is made in the series solution of the number of exposed individuals. The series solutions for the number of deviant people, the number of nondeviant people, the number of people quarantined, and the number of people recovered using the FPSM are unquestionably almost identical to the series solutions for same subgroups using the RPSM, with the exception that these series solutions have initial conditions of the subgroup of the population size. It is observed that, in this paper, the series solutions of the nonlinear system of fractional partial differential equations (PDEs) provided by the RPSM are more in line with the field data than the series solutions provided by the FPSM.

NON-LINEAR OPERATOR APPROXIMATIONS FOR INITIAL VALUE PROBLEMS

Time-evolution of partial differential equations is fundamental for modeling several complex dynamical processes and events forecasting, but the operators associated with such problems are non-linear. We propose a Padé approximation based exponential neural operator scheme for efficiently learning the map between a given initial condition and the activities at a later time. The multiwavelets bases are used for space discretization. By explicitly embedding the exponential operators in the model, we reduce the training parameters and make it more data-efficient which is essential in dealing with scarce and noisy real-world datasets. The Padé exponential operator uses a recurrent structure with shared parameters to model the non-linearity compared to recent neural operators that rely on using multiple linear operator layers in succession. We show theoretically that the gradients associated with the recurrent Padé network are bounded across the recurrent horizon. We perform experiments on non-linear systems such as Korteweg-de Vries (KdV) and Kuramoto-Sivashinsky (KS) equations to show that the proposed approach achieves the best performance and at the same time is data-efficient. We also show that urgent real-world problems like epidemic forecasting (for example, COVID-19) can be formulated as a 2D time-varying operator problem. The proposed Padé exponential operators yield better prediction results (53% (52%) better MAE than best neural operator (non-neural operator deep learning model)) compared to state-of-the-art forecasting models. © 2022 ICLR 2022 - 10th International Conference on Learning Representationss. All rights reserved.

On a global continuum model for COVID-19 virus in the presence of vaccine and induced immunity. Stability and initial states control

The dynamics of COVID-19 virus were investigated in the literature via mathematical models. These models take into account the action of the suspected-exposed-infected-recovered people (SEIR). Also, among them, those which account for quarantined, social distancing functions or health isolation, were presented. In the absence of effective vaccines or therapies, prevention and treatment strategies for COVID-19 infections can not issue to non-epidemic state. Over the world, vaccination against the virus is set on. This motivated us to develop a model for inspecting if this treatment will issue to non endemic state. To this end, a global continuum model for the dynamics of this virus in the presence of vaccine and stimulated immunity is constructed. The present model deals with EIR - deceased individuals (EIRD) together with action of the health isolation and travelers (HIT). Which is described by nonlinear dynamical system (NLDS). Our aim here is to reduce the problem of solving this system to the case of solving LDS. This is carried by introducing the unified method (UM) via an approach present by the authors. By the UM, the solutions of a NLDS are recast to solutions of LDS via auxiliary equations. Numerical results of the exact solutions are evaluated, with initial data for the EIRD together with the number of vaccinated people. Real data are taken from Egypt (can be from elsewhere) at the end of the first wave, and they are considered as the initial conditions. These results are compared with a previous work by the authors in the absence of vaccination. The results of exposed, infected, recovered and deceased people are computed. It is found that the number of infected people decays to zero asymptotically, while, the number of infected people decays to an asymptotic value. This is in contrast to the results found previously in the case of absence of vaccination, where, these numbers grow monotonically. This is completely new. It is shown that locking-down has a remarkable effect in diminishing the number of infected people. The region of initial conditions for I-E people, that guarantee non-epidemic, non-endemic states, is determined via initial states control analysis. A software tool, based on this model, for simplifying the utilization of various data of different countries is developed. It is worth to mention that, the exact solutions of nonlinear dynamical equations, found here, are novel. © 2022

Being a NEET before and after the Great Recession: persistence by gender in Southern Europe

This article adds to the scant literature on the time persistence of being a young Not in Employment, Education or Training (NEET) by including four main novelties: we distinguish short- and long-term persistence;we use estimations before (2004-2007) and after the Great Recession (2013-2016);we analyse four Southern European countries that are relatively similar and were significantly affected by the Great Recession (Greece, Italy, Portugal and Spain);and all analyses are disaggregated by gender. The descriptive analysis shows a convergence in NEET rates by gender in the four countries due to a worsening of the male NEET rate and no improvement among young females. The econometric estimations show that long-term persistence is smaller than short-term persistence and that the latter increased after the Great Recession, especially for male NEETs. Policy implications for the design of the Youth Guarantee and lessons from the coronavirus pandemic are also discussed.

An Equifinality Energy Management Framework in Terms of Benchmarking Practices and Expectations: The EnerMan Project Outlook

Background: The Industry 4.0 wave is leading the changes in existing manufacturing and industrial processes across the world. This is especially important in the formulation of the smart-factory concept with an outlook to energy sustainable processes. In viewing and identifying the foundational elements of such a transformation, the initial conditions and current practices in a cross-sectoral manner is considered a first, yet crucial step in the EU-funded project EnerMan. Methods: In this paper, we identify and analyse the key common features and characteristics of industrial practices set in a perspective of similar and identical functions with a focus to three key energy areas: sustainability, management, and footprint. The examination of different industrial sector cases is performed via distributed questionnaires and then viewed under the prism of the equifinality state via a text-mining analysis approach. Results: identification of common themes and benchmarking of current practices in a cross-industry manner led to the creation of a common systemic framework within energy management related aspects, which is hereby presented. Conclusions: use of an equifinality approach in energy management practices should be further pursued to open up new methods of ideation and innovation and communicate systems’ design in tandem with each industrial set goals.