Global stability and bifurcation analysis of a discrete time SIR epidemic model

Gümüş, Özlem Ak; Cui, Qianqian; Selvam, A. George Maria; Vianny, Abraham

doi:10.18514/mmn.2022.3417

Cited by 6 publications

(4 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If the change is discrete, it would be more appropriate to use difference equations for modelling. Moreover, these equations provide a more realistic approach to describe events with different characteristic processes, while retaining the essential properties of the corresponding continuous time models, [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. For this purpose, we provide more recent articles as references [30][31][32].…”

Section: Introductionmentioning

confidence: 99%

Analyses of the SIR Epidemic Model Including Treatment and Immigration

Ak Gümüş,

Selvam,

Kılınç

et al. 2024

Journal of Mathematical Sciences and Modelling

Self Cite

View full text Add to dashboard Cite

This paper aims to examine the dynamics of a variation of a nonlinear SIR epidemic model. We analyze the complex dynamic nature of the discrete time SIR epidemic model by discretizing a continuous SIR epidemic model subject to treatment and immigration effects with the Euler method. First of all, we show the existence of equilibrium points of the model by reducing the three-dimensional system to the two-dimensional system. Next, we show the stability conditions of the obtained positive equilibrium point and the visibility of Flip and Neimark-Sacker bifurcation. We also perform numerical simulations to support analytical results. We do all these analyzes for models with and without immigration; and shows the effect of immigration on dynamics.

show abstract

Section: Introductionmentioning

confidence: 99%

Analyses of the SIR Epidemic Model Including Treatment and Immigration

Ak Gümüş,

Selvam,

Kılınç

et al. 2024

Journal of Mathematical Sciences and Modelling

Self Cite

View full text Add to dashboard Cite

show abstract

“…The Standard Finite Difference method, NSFD method, and analytical solution are presented. More recent studies about the stability analysis of the mathematical models are presented in [36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

An Application of Nonstandard Finite Difference Method to a Model Describing Diabetes Mellitus and Its Complications

TURHAN ÇETİNKAYA

2023

Journal of New Theory

View full text Add to dashboard Cite

In this study, a mathematical model describing diabetes mellitus and its complications in a population is considered. Since standard numerical methods can lead to numerical instabilities, it aims to solve the problem using a nonstandard method. Among the nonstandard methods, nonstandard finite difference (NSFD) schemes that satisfy dynamical consistency are preferred to make the model discrete. Both continuous and discrete models are analyzed to show the stability of the model at the equilibrium points. The Schur-Cohn criterion is used to perform stability analysis at the equilibrium point of the discretized model. Thus, asymptotically stability of the model is presented. Moreover, the advantages of the NSFD method are emphasized by comparing the stability for different step sizes with classical methods, such as Euler and Runge-Kutta. It has been observed that the NSFD method is convergence for larger step sizes. In addition, the numerical results obtained by NSFD schemes are compared with the Runge–Kutta–Fehlberg (RKF45) method in graphical forms. The accuracy of the NSFD method is observed.

show abstract

“…Discrete-time models allow random time step units for non-overlapping generations. These models are more realistic for a description of processes with different characteristic times which can retain the essential features of the corresponding continuous-time models and include richer applications [13,[19][20][21][22][23][24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Neimark-Sacker Bifurcation and Control of Chaotic Behavior in a Discrete-Time Plant-Herbivore System

2022

View full text Add to dashboard Cite

In this study, the dynamics of a discrete-time plant-herbivore model obtained using the forward Euler method are discussed. The existence of fixed points is investigated. A topological classification is made to examine the behavior of the positive fixed point where the plant and the herbivore coexist. In addition, the existence conditions and direction of Neimark-Sacker bifurcation of the model are investigated using bifurcation theory. Hybrid control method is applied to control the chaos caused by Neimark-Sacker bifurcation. Examples including time series figures, bifurcation figures, phase portraits and maximum Lyapunov exponent are provided to support our theoretical results.

show abstract

Global stability and bifurcation analysis of a discrete time SIR epidemic model

Cited by 6 publications

References 11 publications

Analyses of the SIR Epidemic Model Including Treatment and Immigration

Analyses of the SIR Epidemic Model Including Treatment and Immigration

An Application of Nonstandard Finite Difference Method to a Model Describing Diabetes Mellitus and Its Complications

Neimark-Sacker Bifurcation and Control of Chaotic Behavior in a Discrete-Time Plant-Herbivore System

Contact Info

Product

Resources

About