Discrete-time COVID-19 epidemic model with chaos, stability and bifurcation

Al-Basyouni, K. S.; Khan, A. Q.

doi:10.1016/j.rinp.2022.106038

Cited by 5 publications

(3 citation statements)

References 13 publications

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“…Remark 1. In previous researches, system selection has mostly been dominated by the ODE model and less by the use of the PDE model [38][39][40][41]. However, the ODE model only describes the temporal dynamics.…”

Section: S T X Y S T X Y I T X Y I T X Ymentioning

confidence: 99%

Complex pattern evolution of a two-dimensional space diffusion model of malware spread

Cheng,

Xiao,

et al. 2024

Phys. Scr.

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In order to investigate the propagation mechanism of malware in cyber-physical systems (CPSs), the cross-diffusion in two-dimensional space is attempted to be introduced into a class of susceptible-infected (SI) malware propagation model depicted by partial differential equations (PDEs). Most of the traditional reaction-diffusion models of malware propagation only take into account the self-diffusion in one-dimensional space, but take less consideration of the cross-diffusion in two-dimensional space. This paper investigates the spatial diffusion behaviour of malware nodes spreading through physical devices. The formations of Turing patterns after homogeneous stationary instability triggered by Turing bifurcation are investigated by linear stability analysis and multiscale analysis methods. The conditions under the occurence of Hopf bifurcation and Turing bifurcation in the malware model are obtained. The amplitude equations are derived in the vicinity of the bifurcation point to explore the conditions for the formation of Turing patterns in two-dimensional space. And the corresponding patterns are obtained by varying the control parameters. It is shown that malicious virus nodes spread in different forms including hexagons, stripes and a mixture of the two. This paper will extend a new direction for the study of system security theory.

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Section: S T X Y S T X Y I T X Y I T X Ymentioning

confidence: 99%

Complex pattern evolution of a two-dimensional space diffusion model of malware spread

Cheng,

Xiao,

et al. 2024

Phys. Scr.

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“…If inequality (13) does not hold for the integrodifference model ( 3), then a plus-one bifurcation will be generated; If inequality (14) does not hold, then a minus-one bifurcation will be generated and a stable two-cycle solution will be formed; If inequality (15) does not hold, then the integrodifference model (3) has a characteristic value at the endemic equilibrium point * E as a complex root, i.e. there is a Hopf bifurcation.…”

Section: Minus-one Bifurcationmentioning

confidence: 99%

“…Discrete-time epidemic models have attracted the attention of many scholars [1]- [13] based on the following facts: 1) Since epidemiological data is often measured in discrete units of time, for example, weekly, or monthly, it is natural to use discrete-time models to describe the spread of epidemics within a population; 2) Discrete-time model exhibit rich dynamic behaviors compared to the corresponding continuous models [14] [15] [16] [17]. As with continuous-time models, a discrete-time model can describe dispersal using continuous space.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Analysis of an SIS Epidemic Integrodifference Model

Zhang,

Cao

2023

JAMP

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In order to analyze the impact of dispersal on disease transmission, we establish an SIS epidemic integrodifference model with a nonlinear incidence function. Firstly, the discrete-time SIS epidemic model is established and studied, including the existence and stability of equilibria, the existence of a flip bifurcation, and chaos. Secondly, the SIS epidemic integrodifference model is built based on the discrete-time SIS epidemic model with dispersal. The dynamic analysis of the model includes the existence and stability of equilibria, the existence of a traveling wave solution, and a minus-one bifurcation. Finally, the results suggest that dispersal causes the system to become more unstable and accelerates the spread of the disease when the equilibrium is unstable. Numerical examples are provided to demonstrate the theoretical results.

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Dynamics behavior of a novel infectious disease model considering population mobility on complex network

Qin,

Yang,

2024

Int. J. Dynam. Control

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Discrete-time COVID-19 epidemic model with chaos, stability and bifurcation

Cited by 5 publications

References 13 publications

Complex pattern evolution of a two-dimensional space diffusion model of malware spread

Complex pattern evolution of a two-dimensional space diffusion model of malware spread

Dynamical Analysis of an SIS Epidemic Integrodifference Model

Dynamics behavior of a novel infectious disease model considering population mobility on complex network

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