接种策略下多菌株SEIR流行病模型的全局稳定性

IF 1.9 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Zakaria Yaagoub, K. Allali
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引用次数: 4

摘要

本文提出并研究了一种具有疫苗接种策略的三株SEIR流行病模型。该模型由九个非线性常微分方程组表示,这些方程组描述了易感个体、菌株-1接种个体、菌株1暴露个体、菌株2暴露个体、菌种3暴露个体、细菌1感染个体、细菌2感染个体、菌株3感染个体和康复个体之间的相互作用。我们从建立所有解的存在性、正性和有界性开始分析这个模型。为了显示全局稳定性,该模型有五个平衡点:第一个代表无病平衡,第二个代表菌株-1的流行平衡,第三个描述菌株-2的平衡,第四个代表菌株-3的平衡点,最后一个被称为总流行平衡。我们使用一些合适的李雅普诺夫函数建立了每个平衡点的全局稳定性。这种稳定性取决于应变-1再现数量R01、应变-2基本再现数量R02和应变-3再现数量R03。数值模拟验证了我们的理论结果。结果表明,为了根除感染,所有菌株的基本繁殖数量必须小于1。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Global Stability of Multi-Strain SEIR Epidemic Model with Vaccination Strategy
A three-strain SEIR epidemic model with a vaccination strategy is suggested and studied in this work. This model is represented by a system of nine nonlinear ordinary differential equations that describe the interaction between susceptible individuals, strain-1-vaccinated individuals, strain-1-exposed individuals, strain-2-exposed individuals, strain-3-exposed individuals, strain-1-infected individuals, strain-2-infected individuals, strain-3-infected individuals, and recovered individuals. We start our analysis of this model by establishing the existence, positivity, and boundedness of all the solutions. In order to show global stability, the model has five equilibrium points: The first one stands for the disease-free equilibrium, the second stands for the strain-1 endemic equilibrium, the third one describes the strain-2 equilibrium, the fourth one represents the strain-3 equilibrium point, and the last one is called the total endemic equilibrium. We establish the global stability of each equilibrium point using some suitable Lyapunov function. This stability depends on the strain-1 reproduction number R01, the strain-2 basic reproduction number R02, and the strain-3 reproduction number R03. Numerical simulations are given to confirm our theoretical results. It is shown that in order to eradicate the infection, the basic reproduction numbers of all the strains must be less than unity.
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来源期刊
Mathematical & Computational Applications
Mathematical & Computational Applications MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-
自引率
10.50%
发文量
86
审稿时长
12 weeks
期刊介绍: Mathematical and Computational Applications (MCA) is devoted to original research in the field of engineering, natural sciences or social sciences where mathematical and/or computational techniques are necessary for solving specific problems. The aim of the journal is to provide a medium by which a wide range of experience can be exchanged among researchers from diverse fields such as engineering (electrical, mechanical, civil, industrial, aeronautical, nuclear etc.), natural sciences (physics, mathematics, chemistry, biology etc.) or social sciences (administrative sciences, economics, political sciences etc.). The papers may be theoretical where mathematics is used in a nontrivial way or computational or combination of both. Each paper submitted will be reviewed and only papers of highest quality that contain original ideas and research will be published. Papers containing only experimental techniques and abstract mathematics without any sign of application are discouraged.
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