Hopf bifurcation analysis of a delayed SEIR epidemic model with infectious force in latent and infected period.

IF 4.1 3区数学 Q1 Mathematics

Advances in Difference Equations Pub Date : 2018-01-01 Epub Date: 2018-10-01 DOI:10.1186/s13662-018-1805-6

Aekabut Sirijampa, Settapat Chinviriyasit, Wirawan Chinviriyasit

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Abstract

In this paper, we analyze a delayed SEIR epidemic model in which the latent and infected states are infective. The model has a globally asymptotically stable disease-free equilibrium whenever a certain epidemiological threshold, known as the basic reproduction number $R_{0}$ , is less than or equal to unity. We investigate the effect of the time delay on the stability of endemic equilibrium when $R_{0} > 1$ . We give criteria that ensure that endemic equilibrium is asymptotically stable for all time delays and a Hopf bifurcation occurs as time delay exceeds the critical value. We give formulae for the direction of Hopf bifurcations and the stability of bifurcated periodic solutions by applying the normal form theory and the center manifold reduction for functional differential equations. Numerical simulations are presented to illustrate the analytical results.

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具有潜伏期和感染期感染力的延迟 SEIR 流行模型的霍普夫分岔分析。

本文分析了一种延迟 SEIR 流行病模型，在该模型中，潜伏状态和感染状态都具有传染性。只要某个流行病学阈值（称为基本繁殖数 R 0）小于或等于一，该模型就有一个全局渐近稳定的无病均衡。我们研究了当 R 0 > 1 时，时间延迟对地方病均衡稳定性的影响。我们给出了一些标准，确保地方性平衡在所有时间延迟下都是渐近稳定的，并且当时间延迟超过临界值时会出现霍普夫分岔。通过应用函数微分方程的正态形式理论和中心流形还原法，我们给出了霍普夫分岔方向和分岔周期解稳定性的公式。我们还给出了数值模拟来说明分析结果。

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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来源期刊

Advances in Difference Equations 数学-数学

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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.