Bifurcation analysis of a SEIR epidemic system with governmental action and individual reaction.

IF 4.1 3区数学 Q1 Mathematics

Advances in Difference Equations Pub Date : 2020-01-01 Epub Date: 2020-10-01 DOI:10.1186/s13662-020-02997-z

Abdelhamid Ajbar, Rubayyi T Alqahtani

引用次数: 5

Abstract

In this paper, the dynamical behavior of a SEIR epidemic system that takes into account governmental action and individual reaction is investigated. The transmission rate takes into account the impact of governmental action modeled as a step function while the decreasing contacts among individuals responding to the severity of the pandemic is modeled as a decreasing exponential function. We show that the proposed model is capable of predicting Hopf bifurcation points for a wide range of physically realistic parameters for the COVID-19 disease. In this regard, the model predicts periodic behavior that emanates from one Hopf point. The model also predicts stable oscillations connecting two Hopf points. The effect of the different model parameters on the existence of such periodic behavior is numerically investigated. Useful diagrams are constructed that delineate the range of periodic behavior predicted by the model.

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具有政府作用和个体反应的SEIR流行病系统的分岔分析。

本文研究了考虑政府作用和个体反应的SEIR流行病系统的动力学行为。传染率考虑了作为阶跃函数建模的政府行动的影响，而响应大流行严重性的个人之间接触减少的模型是作为递减指数函数建模的。我们表明，所提出的模型能够预测COVID-19疾病的各种物理现实参数的Hopf分岔点。在这方面，该模型预测了从一个Hopf点发出的周期性行为。该模型还预测了连接两个Hopf点的稳定振荡。数值研究了不同模型参数对这种周期行为存在性的影响。构建了有用的图表，描绘了模型预测的周期行为的范围。

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

自引率

0.00%

发文量

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.