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.

scholarly journals A study on the AH1N1/09 influenza transmission model with the fractional Caputo–Fabrizio derivative

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shahram Rezapour ◽  
Hakimeh Mohammadi
Keyword(s):  
Fractional Order ◽  
Fixed Point Theory ◽  
Equilibrium Points ◽  
Point Theory ◽  
Euler Method ◽  
Transmission Model ◽  
Order Model ◽  
Influenza Transmission ◽  
The Stability ◽  
Disease Free

Abstract We study the SEIR epidemic model for the spread of AH1N1 influenza using the Caputo–Fabrizio fractional-order derivative. The reproduction number of system and equilibrium points are calculated, and the stability of the disease-free equilibrium point is investigated. We prove the existence of solution for the model by using fixed point theory. Using the fractional Euler method, we get an approximate solution to the model. In the numerical section, we present a simulation to examine the system, in which we calculate equilibrium points of the system and examine the behavior of the resulting functions at the equilibrium points. By calculating the results of the model for different fractional order, we examine the effect of the derivative order on the behavior of the resulting functions and obtained numerical values. We also calculate the results of the integer-order model and examine their differences with the results of the fractional-order model.

scholarly journals A new mathematical model for Zika virus transmission

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shahram Rezapour ◽  
Hakimeh Mohammadi ◽  
Amin Jajarmi
Keyword(s):  
Mathematical Model ◽  
Fractional Order ◽  
Zika Virus ◽  
Fixed Point Theory ◽  
Equilibrium Points ◽  
Virus Transmission ◽  
Point Theory ◽  
Euler Method ◽  
Order Derivative ◽  
The Stability

Abstract We present a new mathematical model for the transmission of Zika virus between humans as well as between humans and mosquitoes. In this way, we use the fractional-order Caputo derivative. The region of the feasibility of system and equilibrium points are calculated, and the stability of equilibrium point is investigated. We prove the existence of a unique solution for the model by using the fixed point theory. By using the fractional Euler method, we get an approximate solution to the model. Numerical results are presented to investigate the effect of fractional derivative on the behavior of functions and also to compare the integer-order derivative and fractional-order derivative results.

scholarly journals On analysis of a nonlinear fractional system for social media addiction involving Atangana–Baleanu–Caputo derivative

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jutarat Kongson ◽  
Weerawat Sudsutad ◽  
Chatthai Thaiprayoon ◽  
Jehad Alzabut ◽  
Chutarat Tearnbucha
Keyword(s):  
Social Media ◽  
Fixed Point Theory ◽  
Equilibrium Points ◽  
Point Theory ◽  
Social Media Addiction ◽  
Proposed Model ◽  
Reproduction Numbers ◽  
The Stability ◽  
Predictor Corrector ◽  
Fractional Orders

AbstractA mathematical model for the dynamic systems of $\mathbb{SMA}$ SMA involving the $\mathbb{ABC}$ ABC -fractional derivative is considered in this manuscript. We examine the basic reproduction number and analyze the stability of the equilibrium points. We prove the theoretical results of the existence and Ulam’s stability of the solutions for the proposed model using fixed point theory and nonlinear analytic techniques. Using the Adams type predictor–corrector rule for the $\mathbb{ABC}$ ABC -fractional integral operator, a numerical scheme is devised for obtaining the approximate solution of the proposed model. Different numerical plots corresponding to various fractional orders are presented. In addition, we demonstrate a numerical simulation for the transmission of social media addiction in two cases with the basic reproduction numbers greater than and less than one.

A malaria model with Caputo–Fabrizio and Atangana–Baleanu derivatives

2021 ◽  
pp. 2150013
Author(s):  
Hamadjam Abboubakar ◽  
Pushpendra Kumar ◽  
Norodin A. Rangaig ◽  
Sachin Kumar
Keyword(s):  
Fixed Point Theory ◽  
Point Theory ◽  
Euler Method ◽  
Lyapunov Theory ◽  
Stability And Convergence ◽  
Uniqueness Of Solutions ◽  
Fractional Models ◽  
Number Formula ◽  
The Stability ◽  
Malaria Model

In this paper, we study two fractional models in the Caputo–Fabrizio sense and Atangana–Baleanu sense, in which the effects of malaria infection on mosquito biting behavior and attractiveness of humans are considered. Using Lyapunov theory, we prove the global asymptotic stability of the unique endemic equilibrium of the integer-order model, and the fractional models, whenever the basic reproduction number [Formula: see text] is greater than one. By using fixed point theory, we prove existence, and conditions of the uniqueness of solutions, as well as the stability and convergence of numerical schemes. Numerical simulations for both models, using fractional Euler method and Adams–Bashforth method, respectively, are provided to confirm the effectiveness of used approximation methods for different values of the fractional-order [Formula: see text].

scholarly journals Dynamical Analysis of SIR Epidemic Model with Nonlinear Pulse Vaccination and Lifelong Immunity

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Wencai Zhao ◽  
Juan Li ◽  
Xinzhu Meng
Keyword(s):  
Periodic Solution ◽  
Epidemic Model ◽  
Fixed Point Theory ◽  
Positive Periodic Solution ◽  
Point Theory ◽  
Dynamical Analysis ◽  
Sir Epidemic Model ◽  
Pulse Vaccination ◽  
Sir Epidemic ◽  
Disease Free

SIR epidemic model with nonlinear pulse vaccination and lifelong immunity is proposed. Due to the limited medical resources, vaccine immunization rate is considered as a nonlinear saturation function. Firstly, by using stroboscopic map and fixed point theory of difference equations, the existence of disease-free periodic solution is discussed, and the globally asymptotical stability of disease-free periodic solution is proven by using Floquet multiplier theory and differential impulsive comparison theorem. Moreover, by using the bifurcation theorem, sufficient condition for the existence of positive periodic solution is obtained by choosing impulsive vaccination period as a bifurcation parameter. Lastly, some simulations are given to validate the theoretical results.

scholarly journals On the probabilistic stability of some functional equations

2013 ◽  
Vol 29 (1) ◽  
pp. 125-132
Author(s):  
CLAUDIA ZAHARIA ◽  
◽  
DOREL MIHET ◽  
Keyword(s):  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Stability Of Functional Equations ◽  
The Stability ◽  
Stability Results

We establish stability results concerning the additive and quadratic functional equations in complete Menger ϕ-normed spaces by using fixed point theory. As particular cases, some theorems regarding the stability of functional equations in β - normed and quasi-normed spaces are obtained.

FRACTIONAL ORDER ANALYSIS OF HBV AND HCV CO-INFECTION UNDER ABC DERIVATIVE

Fractals ◽  
2021 ◽  
Author(s):  
HUSSAM ALRABAIAH ◽  
MATI UR RAHMAN ◽  
IBRAHIM MAHARIQ ◽  
SAMIA BUSHNAQ ◽  
MUHAMMAD ARFAN
Keyword(s):  
Mathematical Model ◽  
Fixed Point ◽  
Approximate Solution ◽  
Fractional Order ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Comparative Result ◽  
Order Analysis ◽  
The Stability ◽  
Fractional Orders

In this paper, we consider a fractional mathematical model describing the co-infection of HBV and HCV under the non-singular Mittag-Leffler derivative. We also investigate the qualitative analysis for at least one solution and a unique solution by applying the approach fixed point theory. For an approximate solution, the technique of the iterative fractional order Adams–Bashforth scheme has been implemented. The simulation for the proposed scheme has been drawn at various fractional order values lying between (0,1) and integer-order of 1 via using Matlab. All the compartments have shown convergence and stability with time. A detailed comparative result has been given by the different fractional orders, which showed that the stability was achieved more rapidly at low orders.

The stability of an additive functional equation in menger probabilistic φ-normed spaces

2011 ◽  
Vol 61 (5) ◽  
Author(s):  
D. Miheţ ◽  
R. Saadati ◽  
S. Vaezpour
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theory ◽  
Stability Result ◽  
Point Theory ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
Probabilistic Normed Spaces ◽  
The Stability

AbstractWe establish a stability result concerning the functional equation: $\sum\limits_{i = 1}^m {f\left( {mx_i + \sum\limits_{j = 1,j \ne i}^m {x_j } } \right) + f\left( {\sum\limits_{i = 1}^m {x_i } } \right) = 2f\left( {\sum\limits_{i = 1}^m {mx_i } } \right)} $ in a large class of complete probabilistic normed spaces, via fixed point theory.

scholarly journals Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Ruofeng Rao ◽  
Shouming Zhong
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Distributed Delay ◽  
Reaction Diffusion ◽  
Cellular Neural Network ◽  
Point Theory ◽  
Complete Space ◽  
Practical Engineering ◽  
The Fixed Point Theorem ◽  
The Stability

This paper investigates the stochastically exponential stability of reaction-diffusion impulsive stochastic cellular neural networks (CNN). The reaction-diffusion pulse stochastic system model characterizes the complexity of practical engineering and brings about mathematical difficulties, too. However, the difficulties have been overcome by constructing a new contraction mapping and an appropriate distance on a product space which is guaranteed to be a complete space. This is the first time to employ the fixed point theorem to derive the stability criterion of reaction-diffusion impulsive stochastic CNN with distributed time delays. Finally, an example is provided to illustrate the effectiveness of the proposed methods.

On the stability of some functional equations in Menger φ-normed spaces

2014 ◽  
Vol 64 (1) ◽  
Author(s):  
Dorel Miheţ ◽  
Reza Saadati
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Additive Functional ◽  
Normed Spaces ◽  
Additive Functional Equation ◽  
The Stability ◽  
Stability Results

AbstractRecently, the authors [MIHEŢ, D.—SAADATI, R.—VAEZPOUR, S. M.: The stability of an additive functional equation in Menger probabilistic φ-normed spaces, Math. Slovaca 61 (2011), 817–826] considered the stability of an additive functional in Menger φ-normed spaces. In this paper, we establish some stability results concerning the cubic, quadratic and quartic functional equations in complete Menger φ-normed spaces via fixed point theory.

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