无标度网络和动态小世界网络上的SEIS及SEIR模型研究

Study on the SEIS and SEIR Models on Scale-free Networks and Dynamic Small-world Networks

在潜伏期患者不具备传染能力的条件下,分析了两类疾病传播模型:易感者-潜伏者-染病者-易感者(SEIS)模型和易感者-潜伏者-染病者-恢复者(SEIR)模型.发现这两类疾病传播模型在无标度网络上的传播阈值与转移概率无关,但达到平衡时感染者的密度随着转移概率的增大而增大.同时,在动态小世界网络上,对SEIS模型而言,疾病传播的阈值条件是β>γ/(1+γ);对SEIR模型而言,疾病传播的阈值条件为p>(1-β)γ/β.

In this paper,under the condition of latent period and no incubation period,we study the epidemic threshold and other properties of two types of disease transmission models：Susceptible-Exposed-InfectedSusceptible（SEIS）model and Susceptible-Exposed-Infected-Recovered（SEIR）model.We find that the epidemic thresholds of these two types of diseases transmission models are independent on the transition probability for the scale-free network.However,when the equilibrium is reached,the density of the infected individual increases with the increase of the transition probability.Furthermore we also find that,for the dynamic small world network,in the SEIS model,the threshold conditions for the spread of the disease isβγ/（1＋γ）;in the SEIR model,the epidemic threshold of diseases transmission is p （1-β）γ/β.