离散时间SEIR模型在COVID-19传播中的应用

IF 0.6 Q3 ENGINEERING, MULTIDISCIPLINARY

Journal of Applied Nonlinear Dynamics Pub Date : 2023-06-01 DOI:10.5890/jand.2023.06.010

U. Rozikov, S. Shoyimardonov

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引用次数: 0

摘要

易感暴露-感染-恢复（SEIR）模型在几个国家应用，以确定2019冠状病毒疾病（新冠肺炎）的传播。我们考虑了一个封闭系统中的离散时间SEIR流行病模型，该模型不考虑出生或死亡，所考虑的总人口规模是恒定的。这个动力系统是由非线性演化算子根据四个参数生成的。在某些参数条件下，我们将演化算子简化为一个二次随机算子（QSO），它将三维单纯形映射到自己。我们证明了QSO具有不可数的不动点集（均位于单纯形的边界上）。结果表明，SEIR模型的动力学系统（由QSO生成）的所有轨迹都是收敛的（即QSO是规则的）。此外，我们还讨论了乌兹别克斯坦模式的效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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An application of discrete-time SEIR model to the COVID-19 spread

The Susceptible-Exposed-Infectious-Recovered (SEIR) model is applied in several countries to ascertain the spread of the coronavirus disease 2019 (COVID-19). We consider discrete-time SEIR epidemic model in a closed system which does not account for births or deaths, total population size under consideration is constant. This dynamical system generated by a non-linear evolution operator depending on four parameters. Under some conditions on parameters we reduce the evolution operator to a quadratic stochastic operator (QSO) which maps 3-dimensional simplex to itself. We show that the QSO has uncountable set of fixed points (all laying on the boundary of the simplex). It is shown that all trajectories of the dynamical system (generated by the QSO) of the SEIR model are convergent (i.e. the QSO is regular). Moreover, we discuss the efficiency of the model for Uzbekistan.

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来源期刊

Journal of Applied Nonlinear Dynamics Engineering-Mechanical Engineering

CiteScore

1.20

自引率

20.00%

发文量

期刊介绍： The aim of the journal is to stimulate more research interest and attention for nonlinear dynamical behaviors and engineering nonlinearity for design. The manuscripts in complex dynamical systems with nonlinearity and chaos are solicited, which includes physical mechanisms of complex systems and engineering applications of nonlinear dynamics. The journal provides a place to researchers for the rapid exchange of ideas and techniques in nonlinear dynamics and engineering nonlinearity for design. Topics of Interest Complex dynamics in engineering Nonlinear vibration and dynamics for design Nonlinear dynamical systems and control Fractional dynamics and applications Chemical dynamics and bio-systems Economical dynamics and predictions Dynamical systems synchronization Bio-mechanical systems and devices Nonlinear structural dynamics Nonlinear multi-body dynamics Multiscale wave propagation in materials Nonlinear rotor dynamics Nonlinear waves and acoustics.