Pattern dynamics and bifurcation in delayed SIR network with diffusion network  

作　　者：Wenjie Yang Qianqian Zheng Jianwei Shen 

机构地区：[1]School of Science,Xuchang University Xuchang,Henan 461000,P.R.China [2]School of Mathematics and Statistics North China University of Water Resources and Electric Power Zhengzhou,Henan 450046,P.R.China

出　　处：《International Journal of Biomathematics》2024年第2期87-111,共25页生物数学学报（英文版）

摘　　要：The spread of infectious diseases often presents the emergent properties,which leads to more dificulties in prevention and treatment.In this paper,the SIR model with both delay and network is investigated to show the emergent properties of the infectious diseases'spread.The stability of the SIR model with a delay and two delay is analyzed to illustrate the effect of delay on the periodic outbreak of the epidemic.Then the stability conditions of Hopf bifurcation are derived by using central manifold to obtain the direction of bifurcation,which is vital for the generation of emergent behavior.Also,numerical simulation shows that the connection probability can affect the types of the spatio-temporal patterns,further induces the emergent properties.Finally,the emergent properties of COVID-19 are explained by the above results.

关 键 词：Pattern dynamics SIR model random network connection probability Hopf bifurcation 

分 类 号：O17[理学—数学]