具有警戒性和疫苗接种的随机流行病模型的预测分析与滑模控制

IF 2.6 4区数学 Q2 MATHEMATICAL & COMPUTATIONAL BIOLOGY

Mathematical Modelling of Natural Phenomena Pub Date : 2023-01-18 DOI:10.1051/mmnp/2023003

Yue Zhang, Xiju Wu

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引用次数: 0

摘要

本文研究了一个具有警戒性和疫苗接种的随机SEIR流行病模型。目标是迅速稳定传染病系统。分析了模型的动态特性，设计了具有分布式补偿的积分滑模控制器。利用李雅普诺夫函数方法，得到了全局正解存在唯一性和遍历平稳分布存在的充分条件。利用随机中心流形和随机平均方法将系统简化为一维马尔可夫扩散过程。利用奇异边界理论分析了系统的随机稳定性和Hopf分岔。采用线性矩阵不等式（LMI）方法设计了一种具有非并行分布补偿的积分滑模控制器，实现了系统的稳定性，防止了流行病的爆发。在MATLAB/Simulink中进行数值仿真，验证了理论分析的正确性和控制器的有效性。

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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FORECAST ANALYSIS AND SLIDING MODE CONTROL ON A STOCHASTIC EPIDEMIC MODEL WITH ALERTNESS AND VACCINATION

In this paper, a stochastic SEIR epidemic model is studied with alertness and vaccination. The goal is to stabilize the infectious disease system quickly. The dynamic behavior of the model is analyzed and an integral sliding mode controller with distributed compensation is designed. By using Lyapunov function method, the sufficient conditions for the existence and uniqueness of global positive solutions and the existence of ergodic stationary distributions are obtained. The stochastic center manifold and stochastic average method are used to simplify the system into a one-dimensional Markov diffusion process. The stochastic stability and Hopf bifurcation are analyzed using singular boundary theory. An integral sliding mode controller with non-parallel distributed compensation is designed by linear matrix inequality (LMI) method, which realizes the stability of system and prevents the outbreak of epidemic disease. The correction of theoretical analysis and the effectiveness of controller are validated using numerical simulation performed in MATLAB/Simulink.

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来源期刊

Mathematical Modelling of Natural Phenomena MATHEMATICAL & COMPUTATIONAL BIOLOGY-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

5.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Mathematical Modelling of Natural Phenomena (MMNP) is an international research journal, which publishes top-level original and review papers, short communications and proceedings on mathematical modelling in biology, medicine, chemistry, physics, and other areas. The scope of the journal is devoted to mathematical modelling with sufficiently advanced model, and the works studying mainly the existence and stability of stationary points of ODE systems are not considered. The scope of the journal also includes applied mathematics and mathematical analysis in the context of its applications to the real world problems. The journal is essentially functioning on the basis of topical issues representing active areas of research. Each topical issue has its own editorial board. The authors are invited to submit papers to the announced issues or to suggest new issues. Journal publishes research articles and reviews within the whole field of mathematical modelling, and it will continue to provide information on the latest trends and developments in this ever-expanding subject.