scholarly journals Fractional-Order Discrete-Time SIR Epidemic Model with Vaccination: Chaos and Complexity

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 165
Author(s):  
Zai-Yin He ◽  
Abderrahmane Abbes ◽  
Hadi Jahanshahi ◽  
Naif D. Alotaibi ◽  
Ye Wang
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Epidemic Model ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Maximum Lyapunov Exponent ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Reasonable Range ◽  
Fractional Orders

This research presents a new fractional-order discrete-time susceptible-infected-recovered (SIR) epidemic model with vaccination. The dynamical behavior of the suggested model is examined analytically and numerically. Through using phase attractors, bifurcation diagrams, maximum Lyapunov exponent and the 0−1 test, it is verified that the newly introduced fractional discrete SIR epidemic model vaccination with both commensurate and incommensurate fractional orders has chaotic behavior. The discrete fractional model gives more complex dynamics for incommensurate fractional orders compared to commensurate fractional orders. The reasonable range of commensurate fractional orders is between γ = 0.8712 and γ = 1, while the reasonable range of incommensurate fractional orders is between γ2 = 0.77 and γ2 = 1. Furthermore, the complexity analysis is performed using approximate entropy (ApEn) and C0 complexity to confirm the existence of chaos. Finally, simulations were carried out on MATLAB to verify the efficacy of the given findings.

scholarly journals Behavior of a Discrete Fractional Order SIR Epidemic Model

2018 ◽  
Vol 7 (4.10) ◽  
pp. 675 ◽  
Author(s):  
A. George Maria Selvam ◽  
D. Abraham Vianny
Keyword(s):  
Equilibrium Point ◽  
Fractional Order ◽  
Epidemic Model ◽  
Dynamical Behavior ◽  
Basic Reproductive Number ◽  
Phase Portraits ◽  
Reproductive Number ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Parameter Values

In this paper we investigate the dynamical behavior of a SIR epidemic model of fractional order. Disease Free Equilibrium point, Endemic Equilibrium point and basic reproductive number are obtained. Time series plots, phase portraits and bifurcation diagrams are presented for suitable parameter values. Also some numerical examples are provided to illustrate the dynamics of the system.  

Stability and Bifurcation Analysis in a Discrete-Time SIR Epidemic Model with Fractional-Order

2019 ◽  
Vol 20 (3-4) ◽  
pp. 339-350 ◽  
Author(s):  
Moustafa El-Shahed ◽  
Ibrahim M. E. Abdelstar
Keyword(s):  
Fractional Order ◽  
Bifurcation Analysis ◽  
Epidemic Model ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Flip Bifurcation ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Stability And Bifurcation ◽  
Stability And Bifurcation Analysis

AbstractIn this paper, the dynamical behavior of a discrete SIR epidemic model with fractional-order with non-monotonic incidence rate is discussed. The sufficient conditions of the locally asymptotic stability and bifurcation analysis of the equilibrium points are also discussed. The numerical simulations come to illustrate the dynamical behaviors of the model such as flip bifurcation, Hopf bifurcation and chaos phenomenon. The results of numerical simulation verify our theoretical results.

scholarly journals Solutions of Conformable Fractional-Order SIR Epidemic Model

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Atimad Harir ◽  
Said Malliani ◽  
Lalla Saadia Chandli
Keyword(s):  
Fractional Order ◽  
Epidemic Model ◽  
Analytic Solution ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Transformation Method ◽  
Conformable Fractional Derivative ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Fractional Differential

In this paper, the conformable fractional-order SIR epidemic model are solved by means of an analytic technique for nonlinear problems, namely, the conformable fractional differential transformation method (CFDTM) and variational iteration method (VIM). These models are nonlinear system of conformable fractional differential equation (CFDE) that has no analytic solution. The VIM is based on conformable fractional derivative and proved. The result revealed that both methods are in agreement and are accurate and efficient for solving systems of OFDE.

scholarly journals Fractional-Order SIR Epidemic Model for Transmission Prediction of COVID-19 Disease

2020 ◽  
Vol 10 (23) ◽  
pp. 8316
Author(s):  
Kamil Kozioł ◽  
Rafał Stanisławski ◽  
Grzegorz Bialic
Keyword(s):  
Fractional Order ◽  
Epidemic Model ◽  
Dynamic Properties ◽  
Sir Model ◽  
Domain Model ◽  
Sir Epidemic Model ◽  
Step Method ◽  
Order Difference ◽  
Sir Epidemic ◽  
The Time Domain

In this paper, the fractional-order generalization of the susceptible-infected-recovered (SIR) epidemic model for predicting the spread of the COVID-19 disease is presented. The time-domain model implementation is based on the fixed-step method using the nabla fractional-order difference defined by Grünwald-Letnikov formula. We study the influence of fractional order values on the dynamic properties of the proposed fractional-order SIR model. In modeling the COVID-19 transmission, the model’s parameters are estimated while using the genetic algorithm. The model prediction results for the spread of COVID-19 in Italy and Spain confirm the usefulness of the introduced methodology.

Global dynamics of a fractional-order SIR epidemic model with memory

2020 ◽  
pp. 2050071 ◽  
Author(s):  
Parvaiz Ahmad Naik
Keyword(s):  
Fractional Derivative ◽  
Memory Effect ◽  
Fractional Order ◽  
Epidemic Model ◽  
Memory Trace ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Global Dynamics ◽  
Sir Epidemic Model ◽  
Sir Epidemic

In this paper, an investigation and analysis of a nonlinear fractional-order SIR epidemic model with Crowley–Martin type functional response and Holling type-II treatment rate are established along the memory. The existence and stability of the equilibrium points are investigated. The sufficient conditions for the persistence of the disease are provided. First, a threshold value, [Formula: see text], is obtained which determines the stability of equilibria, then model equilibria are determined and their stability analysis is considered by using fractional Routh-Hurwitz stability criterion and fractional La-Salle invariant principle. The fractional derivative is taken in Caputo sense and the numerical solution of the model is obtained by L1 scheme which involves the memory trace that can capture and integrate all past activity. Meanwhile, by using Lyapunov functional approach, the global dynamics of the endemic equilibrium point is discussed. Further, some numerical simulations are performed to illustrate the effectiveness of the theoretical results obtained. The outcome of the study reveals that the applied L1 scheme is computationally very strong and effective to analyze fractional-order differential equations arising in disease dynamics. The results show that order of the fractional derivative has a significant effect on the dynamic process. Also, from the results, it is obvious that the memory effect is zero for [Formula: see text]. When the fractional-order [Formula: see text] is decreased from [Formula: see text] the memory trace nonlinearly increases from [Formula: see text], and its dynamics strongly depends on time. The memory effect points out the difference between the derivatives of the fractional-order and integer order.

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