复杂网络上带直接免疫及传染媒介的SIRS模型  

AN SIRS MODEL WITH DIRECT IMMUNISATION AND INFECTIVE MEDIUM ON COMPLEX NETWORKS

作　　者：万青松[1] 龚明[2,3] 

机构地区：[1]九江职业技术学院信息工程系,江西九江332007 [2]华中科技大学计算机学院,湖北武汉430074 [3]深圳市翠园中学计算机室,广东深圳518003

出　　处：《计算机应用与软件》2014年第9期276-278,293,共4页Computer Applications and Software

基　　金：国家自然科学基金项目(60573120)

摘　　要：复杂网络模拟实际系统时,常采用带有直接免疫的传染模型或带传染媒介的传染模型。这些模型只侧重实际系统的某一方面的因素。针对这一不足,提出一个新的SIRS类传染病模型,即带有传染媒介和直接免疫的SIRS模型。利用平均场理论建立相应的常微分方程系统,并讨论该类系统的传播动力学行为。研究结果表明,均匀网络情况下,该模型存在一个有限的传播阈值,并且传染媒介也会加速疾病的传播;非均匀网络情形时,传播阈值主要与网络的拓扑结构有关。When simulating practical system with complex networks,it usually uses the infection models with either direct immunisation orinfective medium.These models only focus on the factor of certain aspect in the practical system.Aiming at this insufficiency,the paper pro-poses a novel SIRS （susceptible infected removed susceptible）epidemic model,i.e.an SIRS model with infective medium and direct im-munisation.By using mean-field theory,we establish a corresponding ordinary differential equation system,and discuss the transmission dy-namics behaviour of the system.Research results show that there is a limited transmission threshold in the model under the condition of uni-form networks,and the infective medium can also accelerate the disease spread,and the transmission threshold of the model in non-uniformnetworks is mainly related to the topology of the networks.

关 键 词：复杂网络 SIRS模型 传染媒介 直接免疫 传播阈值 

分 类 号：O157.5[理学—数学] TP393[理学—基础数学]