Numerical Simulation and Stability Analysis for the Fractional-Order Dynamics of COVID-19
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.
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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.
65 citations
TL;DR: In this paper, a novel emotion care scheme has been proposed in this paper to analyze multimodal textual data contained in real-time tweets related to COVID-19, where 8-scale emotions (Anger, Anticipation, Disgust, Fear, Joy, Sadness, Surprise, and Trust) over multiple categories such as nature, lockdown, health, education, market, and politics were analyzed.
Abstract: At the dawn of the year 2020, the world was hit by a significant pandemic COVID-19, that traumatized the entire planet. The infectious spread grew in leaps and bounds and forced the policymakers and governments to move towards lockdown. The lockdown further compelled people to stay under house arrest, which further resulted in an outbreak of emotions on social media platforms. Perceiving people's emotional state during these times becomes critically and strategically important for the government and the policymakers. In this regard, a novel emotion care scheme has been proposed in this paper to analyze multimodal textual data contained in real-time tweets related to COVID-19. Moreover, this paper studies 8-scale emotions (Anger, Anticipation, Disgust, Fear, Joy, Sadness, Surprise, and Trust) over multiple categories such as nature, lockdown, health, education, market, and politics. This is the first of its kind linguistic analysis on multiple modes pertaining to the pandemic to the best of our understanding. Taking India as a case study, we inferred from this textual analysis that 'joy' has been lesser towards everything (~9-15%) but nature (~17%) due to the apparent fact of lessened pollution. The education system entailed more trust (~29%) due to teachers' fraternity's consistent efforts. The health sector witnessed sadness (~16%) and fear (~18%) as the dominant emotions among the masses as human lives were at stake. Additionally, the state-wise and emotion-wise depiction is also provided. An interactive internet application has also been developed for the same.
45 citations
TL;DR: In this paper, the population dynamics model including the predator-prey problem and the logistic equation are generalized by using fractional operator in term of Caputo-Fabrizio derivative (CF-derivative).
Abstract: In this research, the population dynamics model including the predator-prey problem and the logistic equation are generalized by using fractional operator in term of Caputo-Fabrizio derivative (CF-derivative). The models under study include of fractional Lotka-Volterra model (FLVM), fractional predator-prey model (FPPM) and fractional logistic model of population growth (FLM-PG) with variable coefficients. After that a numerical scheme is presented to obtain numerical solutions of these fractional models. These solutions are made using three-step Adams-Bashforth scheme. To show the efficiency and the accuracy of the present scheme, a few examples are evaluated. The numerical simulations of the results are depicted the accuracy of the present scheme.
36 citations
TL;DR: A piecewise numerical approach is presented to derive numerical solutions of piecewise modeling models and is concluded that this concept is a new window that will help mankind to better understand nature.
Abstract: Several collected data representing the spread of some infectious diseases have demonstrated that the spread does not really exhibit homogeneous spread. Clear examples can include the spread of Spanish flu and Covid-19. Collected data depicting numbers of daily new infections in the case of Covid-19 from countries like Turkey, Spain show three waves with different spread patterns, a clear indication of crossover behaviors. While modelers have suggested many mathematical models to depicting these behaviors, it becomes clear that their mathematical models cannot really capture the crossover behaviors, especially passage from deterministic resetting to stochastics. Very recently Atangana and Seda have suggested a concept of piecewise modeling consisting in defining a differential operator piece-wisely. The idea was first applied in chaos and outstanding patterns were captured. In this paper, we extend this concept to the field of epidemiology with the aim to depict waves with different patterns. Due to the novelty of this concept, a different approach to insure the existence and uniqueness of system solutions are presented. A piecewise numerical approach is presented to derive numerical solutions of such models. An illustrative example is presented and compared with collected data from 3 different countries including Turkey, Spain and Czechia. The obtained results let no doubt for us to conclude that this concept is a new window that will help mankind to better understand nature.
35 citations
TL;DR: In this paper, a mathematical model of brain tumor growth and diffusion is presented, which is an extension of a simple two-dimensional mathematical model derived from fractional operator in terms of Caputo which is called the fractional Burgess equations (FBEs).
Abstract: In this paper, we present a mathematical model of brain tumor. This model is an extension of a simple two-dimensional mathematical model of glioma growth and diffusion which is derived from fractional operator in terms of Caputo which is called the fractional Burgess equations (FBEs). To obtain a solution for this model, a numerical technique is presented which is based on operational matrix. First, we assume the solution of the problem under the study is as an expansion of the Bernoulli polynomials. Then with combination of the operational matrix based on the Bernoulli polynomials and collocation method, the problem under the study is changed to a system of nonlinear algebraic equations. Finally, the proposed technique is simulated and tested on three types of the FBEs to confirm the superiority and accuracy.
29 citations
References
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Proceedings Article•
01 Jan 1996
TL;DR: In this article, stability results for finite-dimensional linear fractional differential systems in state-space form are given for both internal and external stability, and the main qualitative result is that stabilities are guaranteed iff the roots of some polynomial lie outside the closed angular sector.
Abstract: In this paper, stability results of main concern for control theory are given for finite-dimensional linear fractional differential systems. For fractional differential systems in state-space form, both internal and external stabilities are investigated. For fractional differential systems in polynomial representation, external stability is thoroughly examined. Our main qualitative result is that stabilities are guaranteed iff the roots of some polynomial lie outside the closed angular sector |arg(σ)| ≤ απ/2, thus generalizing in a stupendous way the well-known results for the integer case α = 1.
1,604 citations
TL;DR: In this paper, the authors describe the mathematical modeling and dynamics of a novel corona virus (2019-nCoV) and present the mathematical results of the model and then formulate a fractional model.
Abstract: The present paper describes the mathematical modeling and dynamics of a novel corona virus (2019-nCoV). We describe the brief details of interaction among the bats and unknown hosts, then among the peoples and the infections reservoir (seafood market). The seafood marked are considered the main source of infection when the bats and the unknown hosts (may be wild animals) leaves the infection there. The purchasing of items from the seafood market by peoples have the ability to infect either asymptomatically or symptomatically. We reduced the model with the assumptions that the seafood market has enough source of infection that can be effective to infect people. We present the mathematical results of the model and then formulate a fractional model. We consider the available infection cases for January 21, 2020, till January 28, 2020 and parameterized the model. We compute the basic reproduction number for the data is R 0 ≈ 2.4829 . The fractional model is then solved numerically by presenting many graphical results, which can be helpful for the infection minimization.
544 citations
TL;DR: A Bats–Hosts–Reservoir–People transmission fractional-order COVID-19 model is analysed for simulating the potential transmission with the thought of individual response and control measures by the government and the effectiveness of preventive measures, predicting future outbreaks and potential control strategies of the disease are estimated.
Abstract: Since the first case of 2019 novel coronavirus disease (COVID-19) detected on 30 January, 2020, in India, the number of cases rapidly increased to 3819 cases including 106 deaths as of 5 April, 2020. Taking this into account, in the present work, we have analysed a Bats–Hosts–Reservoir–People transmission fractional-order COVID-19 model for simulating the potential transmission with the thought of individual response and control measures by the government. The real data available about number of infected cases from 14 March, 2000 to 26 March, 2020 is analysed and, accordingly, various parameters of the model are estimated or fitted. The Picard successive approximation technique and Banach’s fixed point theory have been used for verification of the existence and stability criteria of the model. Further, we conduct stability analysis for both disease-free and endemic equilibrium states. On the basis of sensitivity analysis and dynamics of the threshold parameter, we estimate the effectiveness of preventive measures, predicting future outbreaks and potential control strategies of the disease using the proposed model. Numerical computations are carried out utilising the iterative Laplace transform method and comparative study of different fractional differential operators is done. The impacts of various biological parameters on transmission dynamics of COVID-19 is investigated. Finally, we illustrate the obtained results graphically.
132 citations
TL;DR: In this paper, the authors established the similar relationship between a fractional differential equation and the corresponding fractional flow under a reasonable condition and proved Audounet-Matignon-Montseny conjecture.
Abstract: Nowadays, it is known that the solution to a fractional differential equation can’t generally define a dynamical system in the sense of semigroup property due to the history memory induced by the weakly singular kernel But we can still establish the similar relationship between a fractional differential equation and the corresponding fractional flow under a reasonable condition In this paper, we firstly present some results on fractional dynamical system defined by the fractional differential equation with Caputo derivative Furthermore, the linearization and stability theorems of the nonlinear fractional system are also shown As a byproduct, we prove Audounet–Matignon–Montseny conjecture Several illustrative examples are given as well to support the theoretical analysis
129 citations
TL;DR: In this paper, the authors studied the Fractional Order (FO) model of HIV/AIDS involving Liouville and Atangana-Baleanu-Caputo derivatives.
Abstract: In this work, we study the Fractional Order (FO) model HIV/AIDS involving the Liouville–Caputo and Atangana–Baleanu–Caputo derivatives. The generalized HIV/AIDS model enable and indicates that some infected specific move from symptomatic phase to the asymptomatic phase in all kind of analysis. Special iterative solutions were obtained by the use of Laplace and Sumudu transform. Existence, uniqueness of the solution and stability criteria for the FO model were obtained by fixed point theorem. For the numerical treatment of generalized HIV/AIDS model, we using Adams methods. Furthermore, the convergency of the numerical solutions were analyzed in detail. Finally, for results illustration numerical simulations are presented.
108 citations