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

Miskolc Mathematical Notes

article

Özlem Ak Gümüs¹  Qianqian Cui²  George Maria Selvam³  Abraham Vianny³ 

[1] Adiyaman University, Faculty of Arts and Sciences, Department of Mathematics, Adiyaman University;School of Mathematics and Statistics, Ningxia University, 750021, Yinchuan;Department of Mathematics, Sacred Heart College

关键词: discrete epidemic model;    stability;    equilibrium point;    bifurcation;    chaos;   

DOI  :  10.18514/MMN.2022.3417

学科分类：数学（综合）

来源: Miskolci Egyetem

【 摘 要 】

In this paper, we study the complex dynamical behaviors of a discrete-time SIR epidemic model. Analysis of the model demonstrates that the Diseases Free Equilibrium (DFE) point is globally asymptotically stable if the basic reproduction number is less than one while the Endemic Equilibrium (EE) point is globally asymptotically stable if the basic reproduction number is greater than one. The results are further substantiated visually with numerical simulations. Furthermore, numerical results demonstrate that the discrete model has more complex dynamical behaviors including multiple periodic orbits, quasi-periodic orbits and chaotic behaviors. The maximum Lyapunov exponent and chaotic attractors also confirm the chaotic dynamical behaviors of the model.

【 授权许可】

CC BY