具有非均匀接触模式的网络传播建模与分析

Modeling and Analysis of Epidemic Spreading on Network with Heterogeneous Contact Pattern

大部分病毒传播模型具有均匀混合假设,即在一个群体中,每个个体有相同的几率被一个与之相邻的被感染节点感染。然而由于个体免疫系统,生活习惯以及对病毒信息预警所持的态度各有不同,个体之间感染病毒的概率也将不尽相同。因此,网络中存在异质接触模式的病毒传播动力过程成为一个新的研究方向。为了研究非均匀接触模式对病毒传播的影响,以SIS模型为基础,在BA无标度网络上结合非均匀平均场理论,提出了一种具有非均匀接触模式(即具有不同特性的人群具有不同的病毒感染率)的改进型SIS模型,分析求解了传播阈值,并通过蒙特卡罗仿真验证了阈值表达式的有效性。仿真结果表明,非均匀接触SIS模型的阈值由两种人口比例按权重构成,且与网络结构参数有关。

Most classical mathematical models of epidemic spreading assume uniform mixing among individuals,namely,each individual has an equal chance of being infected by an infected neighbor in a population.However,due to the body’s immunologic system,habits and the attitude of the early virus warning,the contact pattern among populations and the individual’s resistance to the epidemic is different.Therefore,the impact of heterogeneous contact pattern on epidemic spreading among populations has become an important research direction.Based on the heterogeneous mean-field method,we propose an improved SIS model with heterogeneous contact pattern on a BA scale-free network,namely,individuals may have different infectious rates and belong to different population groups.The epidemic threshold is analyzed and solved,and the validity of the expression is verified by Monte Carlo simulation.It is found that the threshold of the heterogeneous contact SIS model is composed of two population proportions according to weight,and is related to the network structure parameters.