具有敏感扩散的SIR斑块模型的全局动力学。

IF 4.1 3区 数学 Q1 Mathematics
Advances in Difference Equations Pub Date : 2012-01-01 Epub Date: 2012-08-01 DOI:10.1186/1687-1847-2012-131
Luju Liu, Weiyun Cai, Yusen Wu
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引用次数: 5

摘要

提出并讨论了具有易感物在两个斑块之间分散的S I R流行病学模型。将基本复制数r01和r02定义为阈值参数。利用合作系统的比较原理,证明了当r01和r02都小于1时,无病平衡点是全局渐近稳定的。如果r01高于1单位,r02低于1单位,则提供s21 * s22 *,疾病在第一个补丁中持续存在。若r02大于1单位,r01小于1单位,且s12 * s11 *,则该疾病在第二个斑块中持续存在。如果r01和r02在单位以上,且进一步满足s21 * > s22 *和s12 * > s11 *,则通过构造Lyapunov函数得到唯一的局部平衡点是全局渐近稳定的。此外,可以得出结论,易感人群的分散不会改变流行病学模型的定性行为。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Global dynamics for an SIR patchy model with susceptibles dispersal.

Global dynamics for an SIR patchy model with susceptibles dispersal.

Global dynamics for an SIR patchy model with susceptibles dispersal.

An S I R epidemiological model with suscptibles dispersal between two patches is addressed and discussed. The basic reproduction numbers R 01 and R 02 are defined as the threshold parameters. It shows that if both R 01 and R 02 are below unity, the disease-free equilibrium is shown to be globally asymptotically stable by using the comparison principle of the cooperative systems. If R 01 is above unity and R 02 is below unity, the disease persists in the first patch provided S 2 1 < S 2 2 . If R 02 is above unity, R 01 is below unity, and S 1 2 < S 1 1 , the disease persists in the second patch. And if R 01 and R 02 are above unity, and further S 2 1 > S 2 2 and S 1 2 > S 1 1 are satisfied, the unique endemic equilibrium is globally asymptotically stable by constructing the Lyapunov function. Furthermore, it follows that the susceptibles dispersal in the population does not alter the qualitative behavior of the epidemiological model.

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来源期刊
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审稿时长
4-8 weeks
期刊介绍: The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions. The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between. The aim of Advances in Difference Equations is to report mainly the new developments in the field of difference equations, and their applications in all fields. We will also consider research articles emphasizing the qualitative behavior of solutions of ordinary, partial, delay, fractional, abstract, stochastic, fuzzy, and set-valued differential equations. Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.
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