摘要
媒体报道对传染病的传播有着一定的影响,但它并不是影响其传播的本质因素.通过建立一个具有分段感染率的传染病模型来刻画媒体报道对传染病传播影响的饱和性.分析了系统各平衡态的局部稳定性,同时利用排除极限环的存在性证明了各平衡态的全局稳定性.最后,通过模拟来验证我们的理论分析.
Media coverage has a certain impact on the spread of infectious diseases.But it is not the essential factor that affects the transmission.An epidemic model with segmented incidence rate was formulated and analyzed to describe the limit of media impact.The local stability of the equilibria was analyzed in terms of the basic reproduction number.The global asymptotic stability of endemic equilibriums could then be obtained by excluding the existence of limit cycle for the system.Finally,we use numerical simulations to test our theoretical analysis.
出处
《数学的实践与认识》
北大核心
2016年第11期218-224,共7页
Mathematics in Practice and Theory
基金
山西省自然科学基金(2012011002-1)
山西省131人才工程项目
山西省留学回国人员科技活动择优资助项目
关键词
媒体影响
饱和效应
传染病模型
全局稳定
media coverage
saturation effect
epidemic model
global stability
