Algebraic form and analysis of SIR epidemic dynamics over probabilistic dynamic networks

作     者：Hongxing Yuan Zengqiang Chen Zhipeng Zhang Rui Zhu Zhongxin Liu Hongxing Yuan;Zengqiang Chen;Zhipeng Zhang;Rui Zhu;Zhongxin Liu

作者机构：College of Artificial IntelligenceNankai UniversityTianjin300350China School of Artificial IntelligenceTiangong UniversityTianjin300387China 

出 版 物：《Control Theory and Technology》 (控制理论与技术（英文版）)

年 卷 期：2023年第21卷第4期

页      面：602-611页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0811[工学-控制科学与工程] 

基　　金：supported by the National Natural Science Foundation of China(Nos.61973175,62203328) the Tianjin Natural Science Foundation(Nos.20JCYBJC01060,21JCQNJC00840) the General Terminal IC Interdisciplinary Science Center of Nankai University. 

主　　题：SIR epidemic Probabilistic dynamic networks Final spreading equilibria Semi-tensor product of matrices Algebraic form 

摘      要：The outbreak of corona virus disease 2019 has profoundly affected people’s way of life.It is increasingly necessary to investigate epidemics over social networks.This paper studies susceptible-infected-removed(SIR)epidemics via the semi-tensor product.First,a formal susceptible-infected-removed epidemic dynamic model over probabilistic dynamic networks(SIRED-PDN)is given.Based on an evolutionary rule,the algebraic form for the dynamics of individual states and network topologies is given,respectively.Second,the SIRED-PDN can be described by a probabilistic mix-valued logical network.After providing an algorithm,all possible final spreading equilibria can be obtained for any given initial epidemic state and network topology by seeking attractors of the network.And the shortest time for all possible initial epidemic state and network topology profiles to evolve to the final spreading equilibria can be obtained by seeking the transient time of the network.Finally,an illustrative example is given to show the effectiveness of our model.