Prediction studies of the epidemic peak of coronavirus disease in Japan: From Caputo derivatives to Atangana–Baleanu derivatives

2021 ◽  
Author(s):  
Pushpendra Kumar ◽  
Norodin A. Rangaig ◽  
Hamadjam Abboubakar ◽  
Anoop Kumar ◽  
A. Manickam
Keyword(s):  
Numerical Simulations ◽  
Fractional Derivatives ◽  
Fixed Point Theory ◽  
Real Data ◽  
Point Theory ◽  
Atypical Pneumonia ◽  
Time Data ◽  
Time Intervals ◽  
Caputo Derivatives ◽  
Parameter Values

New atypical pneumonia caused by a virus called Coronavirus (COVID-19) appeared in Wuhan, China in December 2019. Unlike previous epidemics due to the severe acute respiratory syndrome (SARS) and the Middle East respiratory syndrome coronavirus (MERS-CoV), COVID-19 has the particularity that it is more contagious than the other previous ones. In this paper, we try to predict the COVID-19 epidemic peak in Japan with the help of real-time data from January 15 to February 29, 2020 with the uses of fractional derivatives, namely, Caputo derivatives, the Caputo–Fabrizio derivatives, and Atangana–Baleanu derivatives in the Caputo sense. The fixed point theory and Picard–Lindel of approach used in this study provide the proof for the existence and uniqueness analysis of the solutions to the noninteger-order models under the investigations. For each fractional model, we propose a numerical scheme as well as prove its stability. Using parameter values estimated from the Japan COVID-19 epidemic real data, we perform numerical simulations to confirm the effectiveness of used approximation methods by numerical simulations for different values of the fractional-order [Formula: see text], and to give the predictions of COVID-19 epidemic peaks in Japan in a specific range of time intervals.

Positive solutions and stability of fuzzy Atangana–Baleanu variable fractional differential equation model for a novel coronavirus (COVID-19)

2021 ◽  
pp. 2150059
Author(s):  
Pratibha Verma ◽  
Manoj Kumar
Keyword(s):  
Positive Solution ◽  
Fractional Derivatives ◽  
Fixed Point Theory ◽  
Fuzzy Variable ◽  
Point Theory ◽  
Equation Model ◽  
Theory Approach ◽  
Fractional Differential ◽  
Novel Coronavirus ◽  
Rassias Stability

This work provides a new fuzzy variable fractional COVID-19 model and uses a variable fractional operator, namely, the fuzzy variable Atangana–Baleanu fractional derivatives in the Caputo sense. Next, we explore the proposed fuzzy variable fractional COVID-19 model using the fixed point theory approach and determine the solution’s existence and uniqueness conditions. We choose an appropriate mapping and with the help of the upper/lower solutions method. We prove the existence of a positive solution for the proposed fuzzy variable fractional COVID-19 model and also obtain the result on the existence of a unique positive solution. Moreover, we discuss the generalized Hyers–Ulam stability and generalized Hyers–Ulam–Rassias stability. Further, we investigate the results on maximum and minimum solutions for the fuzzy variable fractional COVID-19 model.

scholarly journals A ROBUST COMPUTATIONAL DYNAMICS OF FRACTIONAL-ORDER SMOKING MODEL WITH RELAPSE HABIT

Fractals ◽  
2021 ◽  
Author(s):  
ANWAR ZEB ◽  
SUNIL KUMAR ◽  
TAREQ SAEED
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Computational Dynamics ◽  
The Social ◽  
Banach Contraction ◽  
Bad Breath ◽  
Predictor Corrector ◽  
Good Agreement

The social habit of smoking has affected the whole world in a social manner. It is the main cause of diseases like cancers, asthma, bad breath, etc., and a source of spreading of infectious diseases like COVID-19. This work is related to an existing smoking model with relapse habit converted in fractional order. First, formulation of fractional-order smoking model is presented and then the dynamics of proposed problem is analyzed. Fixed-point theory via Banach contraction and Schauder theorems is used to derive the existence and uniqueness of the model. At last, the adaptive predictor–corrector algorithm and Runge–Kutta fourth-order (RK4) strategy are used to perform simulation. To bolster the validity of the theoretical results, a set of numerical simulations are performed. A good agreement between hypothetical and numerical results is demonstrated via numerical simulations using MATLAB software.

A new modeling and existence–uniqueness analysis for Babesiosis disease of fractional order

2021 ◽  
pp. 2150443
Author(s):  
Rajarama Mohan Jena ◽  
Snehashish Chakraverty ◽  
Mehmet Yavuz ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Fractional Derivative ◽  
Numerical Simulations ◽  
Arbitrary Order ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Qualitative Properties ◽  
Diseased Animal ◽  
Transform Method ◽  
Homotopy Perturbation

In this study, we consider the dynamics of the Babesiosis transmission on bovine populations and ticks. The most important role in the transmission of the parasite is the ticks from the Ixodidae family. The vector tick takes factors (merozoites in erythrocytes) from the diseased animal while sucking the blood. To model and investigate the transmissions of this parasite and address this important issue, we have considered the disease in a fractional epidemiological model. This paper, therefore, discusses the mechanisms of transmission of Babesiosis defined in the fractional derivative sense. The Caputo–Fabrizio (CF) derivative is considered to study the propagation mechanisms of Babesiosis. First, the important characteristics of the model have been presented, and then the transmission of the Babesiosis model defined in CF is discussed. The application of fixed-point theory is used to derive the concept of the qualitative properties of the mentioned model. The solution is obtained by using the Homotopy perturbation Elzaki transform method (HPETM). Numerical simulations are performed, and the effects of the arbitrary-order derivatives are investigated graphically.

Singular and Non-Singular Kernels Aspect of Time-Fractional Coupled Spring-Mass System

2021 ◽  
Author(s):  
Rajarama Mohan Jena ◽  
Snehashish Chakraverty
Keyword(s):  
Fractional Derivatives ◽  
Polynomial Interpolation ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Mass System ◽  
Dynamical Behaviors ◽  
Uniqueness Of The Solution ◽  
Singular Kernels ◽  
Local Operators ◽  
Non Local

Abstract Dynamical behaviors of the time-fractional nonlinear model of the coupled spring-mass system with damping have been explored here. Fractional derivatives with singular and non-singular kernels are used to assess the suggested model. The fractional Adams-Bashforth numerical method based on Lagrange polynomial interpolation is applied to solve the system with non-local operators. Existence, Ulam-Hyers stability, and uniqueness of the solution are established by using fixed-point theory and nonlinear analysis. Further, the error analysis of the present method has also been included. Finally, the behavior of the solution is explained by graphical representations through numerical simulations.

scholarly journals On a system of Riemann–Liouville fractional differential equations with coupled nonlocal boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rodica Luca
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Fixed Point Theory ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Point Theory ◽  
Fractional Integrals ◽  
Fractional Differential

AbstractWe investigate the existence of solutions for a system of Riemann–Liouville fractional differential equations with nonlinearities dependent on fractional integrals, subject to coupled nonlocal boundary conditions which contain various fractional derivatives and Riemann–Stieltjes integrals. In the proof of our main results, we use some theorems from the fixed point theory.

scholarly journals A Fractional Epidemic Model with Mittag-Leffler Kernel for COVID-19

2021 ◽  
Vol 16 (1) ◽  
pp. 39-56
Author(s):  
Hassan Aghdaoui ◽  
Mouhcine Tilioua ◽  
Kottakkaran Sooppy Nisar ◽  
Ilyas Khan
Keyword(s):  
Numerical Simulations ◽  
Epidemic Model ◽  
Fractional Derivatives ◽  
Real Data ◽  
Disease Evolution ◽  
Seir Model ◽  
The Real ◽  
Stability Results ◽  
Positivity And Boundedness

The aim is to explore a COVID-19 SEIR model involving Atangana-Baleanu Caputo type (ABC) fractional derivatives. Existence, uniqueness, positivity, and boundedness of the solutions for the model are established. Some stability results of the proposed system are also presented. Numerical simulations results obtained in this paper, according to the real data, show that the model is more suitable for the disease evolution.

scholarly journals Mathematical Modeling and Forecasting of COVID-19 in Saudi Arabia under Fractal-Fractional Derivative in Caputo Sense with Power-Law

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 228
Author(s):  
Mdi Begum Jeelani ◽  
Abeer S. Alnahdi ◽  
Mohammed S. Abdo ◽  
Mansour A. Abdulwasaa ◽  
Kamal Shah ◽  
...  
Keyword(s):  
Saudi Arabia ◽  
Fractional Order ◽  
Power Law ◽  
Reproduction Number ◽  
Fixed Point Theory ◽  
Fractal Dimensions ◽  
Real Data ◽  
Point Theory ◽  
Modeling And Forecasting ◽  
Uniqueness Of The Solution

This manuscript is devoted to investigating a fractional-order mathematical model of COVID-19. The corresponding derivative is taken in Caputo sense with power-law of fractional order μ and fractal dimension χ. We give some detailed analysis on the existence and uniqueness of the solution to the proposed problem. Furthermore, some results regarding basic reproduction number and stability are given. For the proposed theoretical analysis, we use fixed point theory while for numerical analysis fractional Adams–Bashforth iterative techniques are utilized. Using our numerical scheme is verified by using some real values of the parameters to plot the approximate solution to the considered model. Graphical presentations corresponding to different values of fractional order and fractal dimensions are given. Moreover, we provide some information regarding the real data of Saudi Arabia from 1 March 2020 till 22 April 2021, then calculated the fatality rates by utilizing the SPSS, Eviews and Expert Modeler procedure. We also built forecasts of infection for the period 23 April 2021 to 30 May 2021, with 95% confidence.

scholarly journals A computational study of transmission dynamics for dengue fever with a fractional approach

2021 ◽  
Author(s):  
Sunil Kumar ◽  
R. P. Chauhan ◽  
Jagdev Singh ◽  
Devendra Kumar
Keyword(s):  
Dengue Fever ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Research Study ◽  
Fixed Point Theory ◽  
Computational Study ◽  
Disease Model ◽  
Point Theory ◽  
Proposed Model ◽  
Predictor Corrector

Fractional derivatives are considered as influential weapon in terms of analysis of infectious disease. The research study in fractional calculus with formulation of new definitions and mathematical tools have a great impact in sector of community health by controlling some fatal diseases. In this article, a generalized version of Caputo derivative which represented as (${}^\mathrm{C}\mathrm{D}_0^{\beta,\sigma}$), is used in alternate modelling of dengue fever disease model. We discuss the existence and uniqueness of solution of model by using fixed point theory. After that, an adaptive predictor-corrector numerical scheme is used to obtain the imminent solution of the proposed model.

Pseudo Almost Automorphic Solution of Semilinear Fractional Differential Equations with the Caputo Derivatives

2015 ◽  
Vol 18 (4) ◽  
Author(s):  
Dingjiang Wang ◽  
Zhinan Xia
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Alternative Theorem ◽  
Caputo Derivatives ◽  
Almost Automorphic ◽  
Fractional Powers Of Operators ◽  
Pseudo Almost Automorphic ◽  
Fractional Differential

AbstractIn this paper, we deal with existence and uniqueness of (μ, ν)-pseudo almost automorphic mild (classical) solution to semilinear fractional differential equations with the Caputo derivatives. The main results are obtained by means of the fixed point theory, Leray-Schauder alternative theorem and fractional powers of operators. Moreover, an application to fractional predator-prey system with diffusion is given.

scholarly journals SEIR epidemic model for COVID-19 transmission by Caputo derivative of fractional order

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shahram Rezapour ◽  
Hakimeh Mohammadi ◽  
Mohammad Esmael Samei
Keyword(s):  
Epidemic Model ◽  
Fixed Point Theory ◽  
Equilibrium Points ◽  
Real Data ◽  
Point Theory ◽  
Euler Method ◽  
Simulation Based ◽  
The World ◽  
Feasibility Region ◽  
The Stability

Abstract We provide a SEIR epidemic model for the spread of COVID-19 using the Caputo fractional derivative. The feasibility region of the system and equilibrium points are calculated and the stability of the equilibrium points is investigated. We prove the existence of a unique solution for the model by using fixed point theory. Using the fractional Euler method, we get an approximate solution to the model. To predict the transmission of COVID-19 in Iran and in the world, we provide a numerical simulation based on real data.

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