离散SIR流行病模型地方性平衡的全局稳定性。

IF 4.1 3区数学 Q1 Mathematics Advances in Difference Equations Pub Date : 2013-01-01 Epub Date: 2013-02-25 DOI:10.1186/1687-1847-2013-42

Xia Ma, Yicang Zhou, Hui Cao

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引用次数: 36

摘要

定义了离散SIR流行病模型的基本繁殖数r0，研究了该模型的动力学行为。证明了当r0 > 1时，无病平衡点是全局渐近稳定的，当r0 > 1时，模型具有持续性。主要关注地方性平衡的全局稳定性。利用比较原理，建立了地方性平衡全局稳定的充分条件。通过数值模拟验证了理论结果和模型的复杂动力学特性。

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Global stability of the endemic equilibrium of a discrete SIR epidemic model.

The basic reproductive number $R_{0}$ of a discrete SIR epidemic model is defined and the dynamical behavior of the model is studied. It is proved that the disease free equilibrium is globally asymptotically stable if $R_{0} < 1$ , and the persistence of the model is obtained when $R_{0} > 1$ . The main attention is paid to the global stability of the endemic equilibrium. Sufficient conditions for the global stability of the endemic equilibrium are established by using the comparison principle. Numerical simulations are done to show our theoretical results and to demonstrate the complicated dynamics of the model.

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来源期刊

Advances in Difference Equations 数学-数学

自引率

0.00%

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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.