Periodic solutions for a seasonally forced SIR model with impact of media coverage

Advances in Difference Equations

Jian Zu¹  Lin Wang² 

[1] Center for Mathematics and Interdisciplinary Sciences, and School of Mathematics and Statistics, Northeast Normal University, Changchun, P.R. China;School of Basic Science, Changchun University of Technology, Changchun, P.R. China

关键词: periodic solution;    SIR model;    media effects;    non-smooth righthand sides;    34C25;    37J45;    92B05;   

DOI  :  10.1186/s13662-015-0477-8

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we study periodic solutions for a seasonally forced SIR model with impact of media coverage. Usually, media reports, information processing, and individuals’ alerted responses to the information can only arise as the number of infected individuals reaches and exceeds a certain level. The piecewise smooth righthand side is introduced to describe the impact of this kind of media coverage. Using Leray-Schauder degree theory, we establish new results on the existence of at least one positive periodic solution for a seasonally forced SIR model with impact of media coverage. Some numerical simulations are presented to illustrate the effectiveness of such media coverage.

【 授权许可】

CC BY