Showing papers in "Results in physics in 2021"
TL;DR: In this paper, a modified SEIR compartmental model accounting for the spread of infection during the latent period, in which they also incorporate effects of varying proportions of containment, was applied to evaluate the confinement rate at the first stages of the epidemic outbreak in order to assess the scenarios that minimize the incidence but also the mortality.
Abstract: After the spread of the SARS-CoV-2 epidemic out of China, evolution in the pandemic worldwide shows dramatic differences among countries. In Europe, the situation of Italy first and later Spain has generated great concen, and despite other countries show better prospects, large uncertainties yet remain on the future evolution and the efficacy of containment, mitigation, or attack strategies. This Manuscript was originally written in the last days of March as a way to report on the first current wave of the pandemic. The results were updated several times for March and also for the month of July. Here we applied a modified SEIR compartmental model accounting for the spread of infection during the latent period, in which we also incorporate effects of varying proportions of containment. We fit data to reported infected populations at the beginning of the first peak of the pandemic to account for the uncertainties in case reporting and study the scenario projections for the individual regions (CCAA). The aim of this model it’s to evaluate the confinement rate at the first stages of the epidemic outbreak in order to assess the scenarios that minimize the incidence but also the mortality. Results indicate that with data for March 23, the epidemics follow an evolution similar to the isolation of 1 , 5 percent of the population, and if there were no effects of intervention actions it might reach a maximum of over 1.4 M infected around April 27. The effect on the epidemics of the ongoing partial confinement measures is yet unknown (an update of results with data until March 31st is included), but increasing the isolation around ten times more could drastically reduce the peak to over 100 k cases by early April, while each day of delay in taking this hard containment scenario represents a 90 percent increase of the infected population at the peak. Dynamics at the sub aggregated levels of CCAA show epidemics at the different levels of progression with the most worrying situation in Madrid and Catalonia. Increasing alpha values up to 10 times, in addition to a drastic reduction in clinical cases, would also more than a half the number of deaths. Updates for March 31st simulations indicate a substantial reduction in burden is underway. A similar approach conducted for Italy pre-and post-intervention also begins to suggest a substantial reduction in both infected and deaths has been achieved, showing the efficacy of drastic social distancing interventions. By last we show the real evolution of the pandemic up to the end of May and the beginning of July in order to calculate the real confinement rate from data to compare with the scenarios formulated at March.
186 citations
TL;DR: In this paper, the sine-Gordon expansion (SGE) approach and the generalized Kudryashov (GK) scheme are used to establish broad-spectral solutions including unknown parameters and typical analytical solutions.
Abstract: The Boussinesq equation simulates weakly nonlinear and long wave approximation that can be used in water waves, coastal engineering, and numerical models for water wave simulation in harbors and shallow seas. In this article, the sine-Gordon expansion (SGE) approach and the generalized Kudryashov (GK) scheme are used to establish broad-spectral solutions including unknown parameters and typical analytical solutions are recovered as a special case. The well-known bell-shape soliton, kink, singular kink, compacton, contracted bell-shape soliton, periodic soliton, anti-bell shape soliton, and other shape solitons are retrieved for the definite value of these constraints. The 3D and contour plots of some of the results obtained are sketched by assigning individual values of the parameter and analyzed the dynamical behavior of the waves. Furthermore, the compatibility of the two approaches has been compared and examined the efficiency to ascertain soliton solutions.
131 citations
TL;DR: In this article, the authors extracted the diverse exact solutions to the conformable time-fractional modified nonlinear Schrodinger equation (CTFMNLSE) that describes the propagation of water waves in the ocean engineering.
Abstract: In this article, our focus is to extract the diverse exact solutions to the conformable time-fractional modified nonlinear Schrodinger equation (CTFMNLSE) that describes the propagation of water waves in the ocean engineering. Diverse exact solutions like trigonometric, hyperbolic and exponential function solutions are extracted. We also secure some other special wave solutions in the forms of shock wave, singular, multiple and mixed complex solitons. The generalized exponential rational function method (GERFM) is used to explain the dynamics of soliton to CTFMNLSE. Furthermore, the constraint conditions for the existence of solutions are reported also singular periodic wave solutions are recovered. Besides, the accomplished solutions are beneficial to interpretation of the wave propagation study and also important for numerical and experimental verifications in ocean engineering
110 citations
TL;DR: Practical significance of predicting COVID-19 cases is elucidated in terms of assessing pandemic characteristics, scenario planning, optimization of models and supporting Sustainable Development Goals (SDGs).
Abstract: The ongoing outbreak of the COVID-19 pandemic prevails as an ultimatum to the global economic growth and henceforth, all of society since neither a curing drug nor a preventing vaccine is discovered. The spread of COVID-19 is increasing day by day, imposing human lives and economy at risk. Due to the increased enormity of the number of COVID-19 cases, the role of Artificial Intelligence (AI) is imperative in the current scenario. AI would be a powerful tool to fight against this pandemic outbreak by predicting the number of cases in advance. Deep learning-based time series techniques are considered to predict world-wide COVID-19 cases in advance for short-term and medium-term dependencies with adaptive learning. Initially, the data pre-processing and feature extraction is made with the real world COVID-19 dataset. Subsequently, the prediction of cumulative confirmed, death and recovered global cases are modelled with Auto-Regressive Integrated Moving Average (ARIMA), Long Short-Term Memory (LSTM), Stacked Long Short-Term Memory (SLSTM) and Prophet approaches. For long-term forecasting of COVID-19 cases, multivariate LSTM models is employed. The performance metrics are computed for all the models and the prediction results are subjected to comparative analysis to identify the most reliable model. From the results, it is evident that the Stacked LSTM algorithm yields higher accuracy with an error of less than 2% as compared to the other considered algorithms for the studied performance metrics. Country-specific analysis and city-specific analysis of COVID-19 cases for India and Chennai, respectively, are predicted and analyzed in detail. Also, statistical hypothesis analysis and correlation analysis are done on the COVID-19 datasets by including the features like temperature, rainfall, population, total infected cases, area and population density during the months of May, June, July and August to find out the best suitable model. Further, practical significance of predicting COVID-19 cases is elucidated in terms of assessing pandemic characteristics, scenario planning, optimization of models and supporting Sustainable Development Goals (SDGs).
99 citations
TL;DR: The research work in this paper attempts to describe the outbreak of Coronavirus Disease 2019 with the help of a mathematical model using both the Ordinary Differential Equation (ODE) and Fractional DifferentialEquation (DFE).
Abstract: The research work in this paper attempts to describe the outbreak of Coronavirus Disease 2019 (COVID-19) with the help of a mathematical model using both the Ordinary Differential Equation (ODE) and Fractional Differential Equation. The spread of the disease has been on the increase across the globe for some time with no end in sight. The research used the data of COVID-19 cases in Nigeria for the numerical simulation which has been fitted to the model. We brought in the consideration of both asymptomatic and symptomatic infected individuals with the fact that an exposed individual is either sent to quarantine first or move to one of the infected classes with the possibility that susceptible individual can also move to quarantined class directly. It was found that the proposed model has two equilibrium points; the disease-free equilibrium point ( DFE ) and the endemic equilibrium point ( E 1 ) . Stability analysis of the equilibrium points shows ( E 0 ) is locally asymptotically stable whenever the basic reproduction number, R 0 1 and ( E 1 ) is globally asymptotically stable whenever R 0 > 1 . Sensitivity analysis of the parameters in the R 0 was conducted and the profile of each state variable was also depicted using the fitted values of the parameters showing the spread of the disease. The most sensitive parameters in the R 0 are the contact rate between susceptible individuals and the rate of transfer of individuals from exposed class to symptomatically infected class. Moreover, the basic reproduction number for the data is calculated as R 0 ≈ 1.7031 . Existence and uniqueness of solution established via the technique of fixed point theorem. Also, using the least square curve fitting method together with the fminsearch function in the MATLAB optimization toolbox, we obtain the best values for some of the unknown biological parameters involved in the proposed model. Furthermore, we solved the fractional model numerically using the Atangana-Toufik numerical scheme and presenting different forms of graphical results that can be useful in minimizing the infection.
87 citations
TL;DR: In this paper, a new and general fractional formulation is presented to investigate the complex behaviors of a capacitor microphone dynamical system, where the classical Euler-Lagrange equations are constructed by using the classical Lagrangian approach.
Abstract: In this study, a new and general fractional formulation is presented to investigate the complex behaviors of a capacitor microphone dynamical system. Initially, for both displacement and electrical charge, the classical Euler–Lagrange equations are constructed by using the classical Lagrangian approach. Expanding this classical scheme in a general fractional framework provides the new fractional Euler–Lagrange equations in which non-integer order derivatives involve a general function as their kernel. Applying an appropriate matrix approximation technique changes the latter fractional formulation into a nonlinear algebraic system. Finally, the derived system is solved numerically with a discussion on its dynamical behaviors. According to the obtained results, various features of the capacitor microphone under study are discovered due to the flexibility in choosing the kernel, unlike the previous mathematical formalism.
86 citations
TL;DR: In this paper, the peak of a solitary wave is weakly affected by the unsmooth boundary, and a fractal variational principle is established to obtain the wave solution in fractal space.
Abstract: It is well-known that the boundary conditions will greatly affect the wave shape of a nonlinear wave equation. This paper reveals that the peak of a solitary wave is weakly affected by the unsmooth boundary. A fractal Korteweg-de Vries (KdV) equation is used as an example to show the solution properties of a solitary wave travelling along an unsmooth boundary. A fractal variational principle is established in a fractal space and its solitary wave solution is obtained, and its wave shape is discussed for different fractal dimensions of the boundary.
83 citations
TL;DR: In this paper, an extended modified auxiliary equation mapping (EMAEMEM) method was employed to the 3D fractional Wazwaz-Benjamin-Bona-Mahony equation (WBBM) with the help of computer symbolic computing system.
Abstract: In this manuscript, we employed an extended modified auxiliary equation mapping (EMAEM) method to the 3D fractional Wazwaz-Benjamin-Bona-Mahony equation (WBBM) with the help of computer symbolic computing system. By using this technique, we get new sets of solutions like kink and anti kink, periodic and doubly periodic, bell shaped, trigonometric functional solutions, hyperbolic solutions, singular kink, rational solutions, and combined soliton like solutions. These results are figured out graphically by using suitable values of parameters with detailed behavior of physical structure of solutions.
79 citations
TL;DR: In this article, a simple graphene metasurface was proposed to achieve obvious graphene plasmon-induced transparency (PIT) phenomenon, which can find that PIT, reflectivity and absorbance can be effectively tuned by the Fermi level.
Abstract: Ultra-high sensitivity sensor has significant application for micro-nano optical devices in terahertz. Here, we propose a simple graphene metasurface, which can achieve obvious graphene plasmon-induced transparency (PIT) phenomenon. We can find that PIT, reflectivity, and absorbance can be effectively tuned by the Fermi level. Moreover, the finite-different time-domain (FDTD) numerical results are well agreement with the coupled mode theory (CMT) results. Interestingly, an ultra-high sensitivity sensor performance based on tunable PIT in terahertz bands can be realized in our proposed metasurface, the sensitivity and Figure of merit (FOM) can reach up to 1.7745 THz/RIU and 23.61, respectively. Hence, these results can provide theoretical guidance for terahertz dynamic integrated photonic devices.
75 citations
TL;DR: In this paper, the exact wave structures to the Gilson-Pickering equation (GPE) were obtained in single and combined behavior like shock, singular, shock-singular, singular periodic waves and periodic rational function by utilizing integration norms.
Abstract: This article possesses new exact wave structures to the Gilson–Pickering equation (GPE) that describes the prorogation of waves in plasma physics. The solutions are achieved in single and combined behavior like shock, singular, shock-singular, singular periodic waves and periodic as well rational function by utilizing innovative integration norms namely ( G ′ G 2 )-expansion method and expansion function method (EFM). Moreover, under the suitable choice of involved parameters 3-, 2-dimensional, and their corresponding contour plots are also sketched. The obtained results show that the applied computational schemes are straightforward, efficient, concise and can be utilized for more complex physical phenomena in various fields of sciences. The reported results are helpful to understand the studying of wave propagation and are also vital for numerical and experimental verification in plasma physics.
74 citations
TL;DR: In this paper, the analytic solutions for different types of nonlinear partial differential equations are obtained using the multiple Exp-function method, which includes three classes of soliton wave solutions in terms of one-wave, two-wave and three-wave solutions.
Abstract: In this work, the analytic solutions for different types of nonlinear partial differential equations are obtained using the multiple Exp-function method. We consider the stated method for the (3+1)-dimensional generalized shallow water-like (SWL) equation, the (3+1)-dimensional Boiti–Leon- Manna–Pempinelli (BLMP) equation, (3+1)-dimensional generalized variable-coefficient B-type Kadomtsev–Petviashvili (VC B-type KP) equation and the (2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada (CDGKS) equation. We obtain multi classes of solutions containing one-soliton, two-soliton, and triple-soliton solutions. All the computations have been performed using the software package Maple. The obtained solutions include three classes of soliton wave solutions in terms of one-wave, two-waves, and three-waves solutions. Then the multiple soliton solutions are presented with more arbitrary autocephalous parameters, in which the one, two, and triple solutions localized in all directions in space. Moreover, the obtained solutions and the exact solutions are shown graphically, highlighting the effects of non-linearity. The different types of obtained solutions of aforementioned nonlinear equations arising in fluid dynamics and nonlinear phenomena.
TL;DR: In this paper, a nonlinear Kadomtsev-Petviashvili equation with a competing dispersion effect is considered and the integrability of the governing equation via using the Painleve analysis is examined.
Abstract: In this paper, we concern ourselves with the nonlinear Kadomtsev–Petviashvili equation (KP) with a competing dispersion effect. First we examine the integrability of governing equation via using the Painleve analysis. We next reduce the KP equation to a one-dimensional with the help of Lie symmetry analysis (LSA). The KP equation reduces to an ODE by employing the Lie symmetry analysis. We formally derive bright, dark and singular soliton solutions of the model. Moreover, we investigate the stability of the corresponding dynamical system via using phase plane theory. Graphical representation of the obtained solitons and phase portrait are illustrated by using Maple software.
TL;DR: In this article, the optical soliton solutions of a nonlinear Schrodinger equation (NLSE) involving parabolic law of nonlinearity with the presence of non linear dispersion were investigated by using the generalized auxiliary equation technique.
Abstract: This paper studies the optical soliton solutions of a nonlinear Schrodinger equation (NLSE) involving parabolic law of nonlinearity with the presence of nonlinear dispersion by using the generalized auxiliary equation technique. As a result, new varieties of exact traveling wave solutions have been uncovered, comprising of the hyperbolic trigonometric, trigonometric, exponential, and rational. Interestingly, we obtain the bright, dark, periodic, singular, and other soliton solutions to the nonlinear model. Some of the achieved solutions are illustrated graphically in order to fully understand their physical behaviour. Furthermore, the findings discussed in this present investigation may be useful in explaining the propagation of optical solitons in a weakly nonlocal parabolic law medium.
TL;DR: In this article, an efficient computational method based on discretization of the domain and memory principle is proposed to solve this fractional-order corona model numerically and the stability of the proposed method is also discussed.
Abstract: The main purpose of this work is to study the dynamics of a fractional-order Covid-19 model. An efficient computational method, which is based on the discretization of the domain and memory principle, is proposed to solve this fractional-order corona model numerically and the stability of the proposed method is also discussed. Efficiency of the proposed method is shown by listing the CPU time. It is shown that this method will work also for long-time behaviour. Numerical results and illustrative graphical simulation are given. The proposed discretization technique involves low computational cost.
TL;DR: In this paper, a simulation study has been carried out at a wide photon energy region in order to investigate the radiation protection feature of bismuth borate glasses, and the results confirm that the parameters of the examined glasses MAC, HVL, TVL, MFP, Zeff, and Neff are associated with photon energy and chemical composition.
Abstract: There has been an increasing number of research and development activities focusing on the use of different glass systems for their nuclear radiation shielding features. In this study a simulation study has been carried out at a wide photon energy region in order to investigate the radiation protection feature of bismuth borate glasses. This study has been conducted to evaluate the proficiency level of six different glass systems (70-x)B2O3 + xBi2O3 + 15ZnO + 15Na2O (where x = 0, 5, 10, 15, 20 and 25 mol%) exposed to photon, charged particle (H1) and (He+2) and neutron. For this investigation, transmission factors (TF), mass attenuation coefficient (MAC), half value layer (HVL), tenth value layer (TVL), mean free path (MFP), effective atomic number (Zeff), effective electron density (Neff) have been computed. The results confirm that the parameters of the examined glasses MAC, HVL, TVL, MFP, Zeff, and Neff are associated with photon energy and chemical composition. In addition, neutron effective cross-sections (∑R) have been computed for bismuth borates and it was seen a good harmony. The computations for present samples have been examined over a broad energy range from 0.01 to 20 MeV and theoretical results have been obtained by using MCNPX software for transmission factors. In addition, simulation results have been calculated with the WinXCom program. Furthermore, MSP and PR calculations of the bismuth borate glass have been performed to figure out the radiation shielding features. For that reason, the SRIM code has been used to simulate H1 and He+2 particles. Considering the results obtained from this research, which examines the radiation protection of bismuth borate glasses, indicates that the best shielding achievement (while the HVL, TVL, MFP, TF have the lowest and the highest (∑R) values) is reached at 25% Bi2O3. As can be seen in the results, the addition of bismuth affirms that the use of such glass systems improves the radiation protection feature. In particular, 25%Bi2O3 glass system has been proved to show superior shielding properties for gamma radiation in combination with charged particles. Since the glass sample with the highest bismuth additive is 25%Bi2O3, the most radiation protection effect is also seen in this example. The obtained material has a satisfactory radiation shielding property as bismuth is added to the mixture.
TL;DR: In this article, a new mathematical model was proposed to investigate the recent outbreak of the coronavirus disease (COVID-19) in the country of Pakistan using stability theory of differential equations and the basic reproductive number that represents an epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix.
Abstract: We propose a new mathematical model to investigate the recent outbreak of the coronavirus disease (COVID-19) The model is studied qualitatively using stability theory of differential equations and the basic reproductive number that represents an epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix The global asymptotic stability conditions for the disease free equilibrium are obtained The real COVID-19 incidence data entries from 01 July, 2020 to 14 August, 2020 in the country of Pakistan are used for parameter estimation thereby getting fitted values for the biological parameters Sensitivity analysis is performed in order to determine the most sensitive parameters in the proposed model To view more features of the state variables in the proposed model, we perform numerical simulations by using different values of some essential parameters Moreover, profiles of the reproduction number through contour plots have been biologically explained
TL;DR: The nabla discrete ABC-fractional operator as more general and applicable in modeling of dynamical problems due to its non-singular kernel and the existence and uniqueness theorems and Hyers-Ulam stability.
Abstract: Microorganisms lives with us in our environment, touching infectious material on the surfaces by hand-mouth which causes infectious diseases and some of these diseases are rapidly spreading from person to person. These days the world facing COVID-19 pandemic disease. This article concerned with existence of results and stability analysis for a nabla discrete ABC-fractional order COVID-19. The nabla discrete ABC-fractional operator as more general and applicable in modeling of dynamical problems due to its non-singular kernel. For the existence and uniqueness theorems and Hyers-Ulam stability, we need to suppose some conditions which will play important role in the proof of our main results. At the end, an expressive example is given to provide an application for the nabla discrete ABC-fractional order COVID-19 model.
TL;DR: A fractional-order SIRD mathematical model of the COVID-19 disease in the sense of Caputo is discussed, which derives the stability results based on the basic reproduction number and proves the results of the solution existence and uniqueness via fixed point theory.
Abstract: We discuss a fractional-order SIRD mathematical model of the COVID-19 disease in the sense of Caputo in this article. We compute the basic reproduction number through the next-generation matrix. We derive the stability results based on the basic reproduction number. We prove the results of the solution existence and uniqueness via fixed point theory. We utilize the fractional Adams–Bashforth method for obtaining the approximate solution of the proposed model. We illustrate the obtained numerical results in plots to show the COVID-19 transmission dynamics. Further, we compare our results with some reported real data against confirmed infected and death cases per day for the initial 67 days in Wuhan city.
TL;DR: In this article, the authors obtained the exact traveling solutions of the M-fractional generalized reaction Duffing model and density dependent diffusion reaction equation by using three fertile expansion methods.
Abstract: In this paper, we obtain the exact traveling solutions of the M-fractional generalized reaction Duffing model and density dependent M-fractional diffusion reaction equation by using three fertile, G ′ / G , 1 / G , modified G ′ / G 2 and 1 / G ′ -expansion methods. These methods contribute a variety of exact traveling wave solutions to the scientific literature. The obtained solutions are also verified for the aforesaid equations through symbolic soft computations. Furthermore, some results are explained through numerical simulations that show the novelty of our work. Moreover, we observe that all the solutions are new and an excellent contribution in the existing literature of solitary wave theory.
TL;DR: In this article, the optical soliton solutions of the generalized non-autonomous nonlinear Schrodinger equation (NLSE) by means of the new Kudryashov method (NKM) were examined with time-dependent coefficients.
Abstract: In this work, we study the optical soliton solutions of the generalized non-autonomous nonlinear Schrodinger equation (NLSE) by means of the new Kudryashov’s method (NKM). The aforesaid model is examined with time-dependent coefficients. We considered three interesting non-Kerr laws which are respectively the quadratic-cubic law, anti-cubic law, andtriple power law. The proposed method, as a newly developed mathematical tool, is efficient, reliable, and a simple approach for computing new solutions to various kinds of nonlinear partial differential equations (NLPDEs) in applied sciences and engineering.
TL;DR: In this article, a detailed analysis of an important class of differential equations called stochastic equations with the new classes of differential operators with the global derivative with integer and non-integer orders is presented.
Abstract: Very recently, the concept of instantaneous change was extended with the aim to accommodate prediction of more complex real world problems that could not be predicted or depicted by the existing rate of change. The extension gave birth to a more general differential operator that to be a derivative associate to the well-known Riemann-Stieltjes integral. In addition to this, using specific functions, one is able to recover all existing local differential operators defined as rate of change. This extended concept is still at its genesis and more works need to be done to establish a Riemann-Stieltjes calculus. In this paper, we aim to present a detailed analysis of an important class of differential equations called stochastic equations with the new classes of differential operators with the global derivative with integer and non-integer orders. We considered many classes as nonlinear Cauchy problems, then we presented existence and the uniqueness of their solutions using the linear growth and the Lipchitz conditions. We derived numerical solutions for each class and presented the error analysis. To show the applicability of these operators, we considered three epidemiological problems, including the zombie virus spread model, the zika virus spread model and Ebola model. We solved each model using the suggested numerical scheme and presented the numerical solutions for different values of fractional order and the global function g t . Our results showed that, more complex real world problems could be depicted using these classes of differential equations.
TL;DR: In this article, the authors evaluated the performance of three deep learning methods and their bidirectional extensions to predict new cases and deaths rate one, three and seven-day ahead during the next 100 days.
Abstract: The first known case of Coronavirus disease 2019 (COVID-19) was identified in December 2019. It has spread worldwide, leading to an ongoing pandemic, imposed restrictions and costs to many countries. Predicting the number of new cases and deaths during this period can be a useful step in predicting the costs and facilities required in the future. The purpose of this study is to predict new cases and deaths rate one, three and seven-day ahead during the next 100 days. The motivation for predicting every n days (instead of just every day) is the investigation of the possibility of computational cost reduction and still achieving reasonable performance. Such a scenario may be encountered in real-time forecasting of time series. Six different deep learning methods are examined on the data adopted from the WHO website. Three methods are LSTM, Convolutional LSTM, and GRU. The bidirectional extension is then considered for each method to forecast the rate of new cases and new deaths in Australia and Iran countries. This study is novel as it carries out a comprehensive evaluation of the aforementioned three deep learning methods and their bidirectional extensions to perform prediction on COVID-19 new cases and new death rate time series. To the best of our knowledge, this is the first time that Bi-GRU and Bi-Conv-LSTM models are used for prediction on COVID-19 new cases and new deaths time series. The evaluation of the methods is presented in the form of graphs and Friedman statistical test. The results show that the bidirectional models have lower errors than other models. A several error evaluation metrics are presented to compare all models, and finally, the superiority of bidirectional methods is determined. This research could be useful for organisations working against COVID-19 and determining their long-term plans.
TL;DR: In this paper, a structural search of the global minimum for bimetallic BeMgn0/− (n = 10 − 20) clusters was performed by utilizing efficient CALYPSO structural searching program with subsequent DFT calculations.
Abstract: Bimetallic clusters have attracted much attention because of the structural and property changes that occur: cluster size and doping. Here, we performed a structural search of the global minimum for bimetallic BeMgn0/− (n = 10–20) clusters by utilizing efficient CALYPSO structural searching program with subsequent DFT calculations. A large number of low energetic isomers converge and the most stable structures are confirmed by comparing the total energies for different cluster sizes. Satisfactory agreement between theoretical and experimental PES spectra demonstrates the validity of our predicted global minimum structures. It is found that the most stable structures of BeMgn0/− clusters are filled cage-like frameworks at n = 10–20. The localized position of Be atoms changes from completely encapsulated sites to surface sites, after which the position reverts to the caged Mg motif. In all BeMgn0/− clusters, the charge transfers from the Mgn motif to Be atoms. Increasing occupations of p orbitals manifest their increasing metallic behaviors. A stability analysis revealed that the D4d symmetric BeMg16 caged structure with one centred Be atom has robust stability, which can be because BeMg16 possesses a closed electronic shell of 1S21P61D101F42S21F10 filled with 34 valence electrons and strong Be-Mg bonds due to s-p hybridization. This finding is supported by multi-centre bonds and Mayer bond order analyses.
TL;DR: In this article, the analytical and semi-analytical solutions of nonlinear phi-four (PF) equation were investigated by applying the sech-tanh expansion method, modified Ψ ′ Ψ -expansion method and Adomian decomposition method.
Abstract: This manuscript investigates the analytical and semi-analytical solutions of nonlinear phi-four (PF) equation by applying the sech–tanh expansion method, modified Ψ ′ Ψ -expansion method and Adomian decomposition method. This equation is considered as a particular case of the well-known Klein–Fock–Gordon (KFG) equation. The KFG equation is derived by Oskar Klein and Walter Gordon and relates to Schrodinger equation. Many quantum effects can be studied based on the PF model’s solutions, such as wave-particle duality to describe reality in the form of waves is at the heart of quantum mechanics. The considered model is also used to explain de Broglie waves’ character, the spineless relativistic composite particles, relativistic electrons, etc., which are also the main icons for a good understanding of the phenomenon of quantum physics. Through two recent analytical schemes, handling this model gives many novel computational solutions that are tested through the semi-analytical scheme to investigate their accuracy. Demonstrating the obtained analytical and matching between analytical and semi-analytical through some distinct sketches shows the considered model’s novel physical properties.
TL;DR: In this article, the authors proposed and extended classical SEIR compartment model refined by contact tracing and hospitalization strategies to explain the COVID-19 outbreak and calibrated their model with daily COVID19 data for the five provinces of India namely, Kerala, Karnataka, Andhra Pradesh, Maharashtra, West Bengal and the overall India.
Abstract: Mathematical modeling plays an important role to better understand the disease dynamics and designing strategies to manage quickly spreading infectious diseases in lack of an effective vaccine or specific antivirals. During this period, forecasting is of utmost priority for health care planning and to combat COVID-19 pandemic. In this study, we proposed and extended classical SEIR compartment model refined by contact tracing and hospitalization strategies to explain the COVID-19 outbreak. We calibrated our model with daily COVID-19 data for the five provinces of India namely, Kerala, Karnataka, Andhra Pradesh, Maharashtra, West Bengal and the overall India. To identify the most effective parameters we conduct a sensitivity analysis by using the partial rank correlation coefficients techniques. The value of those sensitive parameters were estimated from the observed data by least square method. We performed sensitivity analysis for R 0 to investigate the relative importance of the system parameters. Also, we computed the sensitivity indices for R 0 to determine the robustness of the model predictions to parameter values. Our study demonstrates that a critically important strategy can be achieved by reducing the disease transmission coefficient β s and clinical outbreak rate q a to control the COVID-19 outbreaks. Performed short-term predictions for the daily and cumulative confirmed cases of COVID-19 outbreak for all the five provinces of India and the overall India exhibited the steady exponential growth of some states and other states showing decays of daily new cases. Long-term predictions for the Republic of India reveals that the COVID-19 cases will exhibit oscillatory dynamics. Our research thus leaves the option open that COVID-19 might become a seasonal disease. Our model simulation demonstrates that the COVID-19 cases across India at the end of September 2020 obey a power law.
TL;DR: In this article, the authors considered a new COVID-19 model with an optimal control analysis when vaccination is present, and they considered four different controls, such as prevention, vaccination control, rapid screening of people in the exposed category and people who are identified as infected without screening.
Abstract: We are considering a new COVID-19 model with an optimal control analysis when vaccination is present. Firstly, we formulate the vaccine-free model and present the associated mathematical results involved. Stability results for R 0 1 are shown. In addition, we frame the model with the vaccination class. We look at the mathematical results with the details of the vaccine model. Additionally, we are considering setting controls to minimize infection spread and control. We consider four different controls, such as prevention, vaccination control, rapid screening of people in the exposed category, and people who are identified as infected without screening. Using the suggested controls, we develop an optimal control model and derive mathematical results from it. In addition, the mathematical model with control and without control is resolved by the forward–backward Runge–Kutta method and presents the results graphically. The results obtained through optimal control suggest that controls can be useful for minimizing infected individuals and improving population health.
TL;DR: This work identifies four main criteria and fifteen sub-criteria based on age, health status, a woman’s status, and the kind of job and indicates that the healthcare personnel, people with high-risk health, elderly people, essential workers, pregnant and lactating mothers are the most prioritized people to take the vaccine dose first.
Abstract: Since the outbreak of COVID-19, most of the countries around the world have been confronting the loss of lives, struggling with several economical parameters, i.e. low GDP growth, increasing unemployment rate, and others. It’s been 11 months since we are struggling with COVID-19 and some of the countries already facing the second wave of COVID-19. To get rid of these problems, inventions of a vaccine and its optimum distribution is a key factor. Many companies are trying to find a vaccine, but for nearly 8 billion people it would be impossible to find a vaccine. Thus, the competition arises, and this competition would be too intense to satisfy all the people of a country with the vaccine. Therefore, at first, governments must identify priority groups for allocating COVID-19 vaccine doses. In this work, we identify four main criteria and fifteen sub-criteria based on age, health status, a woman’s status, and the kind of job. The main and sub-criteria will be evaluated using a neutrosophic Analytic Hierarchy Process (AHP). Then, the COVID-19 vaccine alternatives will be ranked using a neutrosophic TOPSIS method. All the results obtained indicate that the healthcare personnel, people with high-risk health, elderly people, essential workers, pregnant and lactating mothers are the most prioritized people to take the vaccine dose first. Also, the results indicate that the most appropriate vaccine for patients and health workers have priority over other alternative vaccines.
TL;DR: In this paper, a fractional-order transmission model is considered to study its dynamical behavior using the real cases reported in Saudia Arabia, where the classical Caputo type derivative of fractional order is used in order to formulate the model.
Abstract: The novel coronavirus disease or COVID-19 is still posing an alarming situation around the globe. The whole world is facing the second wave of this novel pandemic. Recently, the researchers are focused to study the complex dynamics and possible control of this global infection. Mathematical modeling is a useful tool and gains much interest in this regard. In this paper, a fractional-order transmission model is considered to study its dynamical behavior using the real cases reported in Saudia Arabia. The classical Caputo type derivative of fractional order is used in order to formulate the model. The transmission of the infection through the environment is taken into consideration. The documented data since March 02, 2020 up to July 31, 2020 are considered for estimation of parameters of system. We have the estimated basic reproduction number ( R 0 ) for the data is 1.2937 . The Banach fixed point analysis has been used for the existence and uniqueness of the solution. The stability analysis at infection free equilibrium and at the endemic state are presented in details via a nonlinear Lyapunov function in conjunction with LaSalle Invariance Principle. An efficient numerical scheme of Adams-Molten type is implemented for the iterative solution of the model, which plays an important role in determining the impact of control measures and also sensitive parameters that can reduce the infection in the general public and thereby reduce the spread of pandemic as shown graphically. We present some graphical results for the model and the effect of the important sensitive parameters for possible infection minimization in the population.
TL;DR: In this article, the perturbed nonlinear Schrodinger-Hirota equation with spatio-temporal dispersion (PNSHE-STD) was investigated using an improved Sardar sub-equation method.
Abstract: The perturbed nonlinear Schrodinger–Hirota equation with spatio-temporal dispersion (PNSHE-STD) which governs the propagation of dispersive pulses in optical fibers, is investigated in this study using an improved Sardar sub-equation method. The Kerr and power laws of nonlinearity are taken into account. As a result of this improved technique, many constraint conditions required for the existence of soliton solutions emerge. We retrieved several solutions such as the bright solitons, dark solitons, singular solitons, mixed bright–dark solitons, singular-bright combo solitons, periodic, and other solutions. Furthermore, we demonstrate the dynamical behaviors and physical significance of these solutions by using different parameter values.
TL;DR: In this paper, an interesting second-order memristor-based map model is constructed to three systems based on Caputo fractional-order difference, and their dynamic behaviors are investigated by the volt-ampere curve, bifurcation diagram, maximum Lyapunov exponent, attractor phase diagram, complexity analysis and basin of attraction.
Abstract: The mathematical modeling of memristor in discrete-time domain is an attractive new issue, but there are still some problems to be explored. This paper studies an interesting second-order memristor-based map model, and the model is constructed to three systems based on Caputo fractional-order difference. Their dynamic behaviors are investigated by the volt–ampere curve, bifurcation diagram, maximum Lyapunov exponent, attractor phase diagram, complexity analysis and basin of attraction. Numerical simulation analysis shows that the fractional-order system exhibits quasi periodic, chaos, coexisting attractors and other complex behaviors, which demonstrates more abundant dynamic behaviors of the fractional-order form. It lays a good foundation for the future analysis or engineering application of the discrete memristor.