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Numerical Simulation and Stability Analysis for the Fractional-Order Dynamics of COVID-19

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TLDR
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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Fractional Model of Ebola Virus In Population of Bats In Frame of Atangana-Baleanu Fractional Derivative

TL;DR: In this article, the authors extend the model of the Ebola virus in bats to the mathematical model of fractional order using Atangana- Baleanu derivative operator and present a detailed proof for the existence, uniqueness, and stability of the solution for the fractional mathematical model is presented.
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Analytical solutions of fractional wave equation with memory effect using the fractional derivative with exponential kernel

TL;DR: In this paper, the authors presented analytical solutions of the fractional wave equation via Caputo-Fabrizio fractional derivative for three cases, the classical, the damped and the damping with a source term defined by the wave equation.
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Power-series solution of compartmental epidemiological models

TL;DR: Power-series solutions of compartmental epidemiological models are used to provide alternate methods to solve the corresponding systems of nonlinear differential equations and a SAIRP compartmental model is analyzed by using the same methodology previously applied to the COVID-19 pandemic.
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Modeling the dynamic of COVID-19 with different types of transmissions

TL;DR: In this article, the authors proposed a new epidemiological mathematical model for the spread of COVID-19 disease with a special focus on the transmissibility of individuals with severe symptoms, mild symptoms, and asymptomatic symptoms.
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A modified variable-order fractional SIR model to predict the spread of COVID-19 in India

TL;DR: In this paper, a variable-order fractional SIR model is proposed to predict the COVID-19 trajectory in India, which can predict the slowing down of the spread between January and February 2021, touching a peak of around 5 lakh confirmed cases.
References
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Proceedings Article

Stability results for fractional differential equations with applications to control processing

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.
Journal ArticleDOI

Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative

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.
Journal ArticleDOI

A mathematical model of COVID-19 using fractional derivative: outbreak in India with dynamics of transmission and control

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.
Journal ArticleDOI

Fractional dynamical system and its linearization theorem

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.
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Stability analysis and numerical solutions of fractional order HIV/AIDS model

TL;DR: In this paper, the authors studied the Fractional Order (FO) model of HIV/AIDS involving Liouville and Atangana-Baleanu-Caputo derivatives.
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