一类传染病模型在有向网络上的传播阈值与免疫策略研究

Study on the Spread Threshold and Immunization Scheme of a Class of Infectious Disease Model on Directed Networks

摘要: 本文将带出生与死亡的传统SIS模型推广到了有向的无标度网络上，计算了模型在常数和线性的网络节点传染力下的地方病平衡点与流行病传播阈值，并且将三种传统的免疫策略植入到模型上面，严格地证明了在三种免疫策略下，模型对传染病的抑制力增加。且在相同的平均免疫率下，进一步比较了三种不同免疫策略的效果，发现免疫出度与入度均大节点的目标免疫在此模型上对疾病的抑制力是最好的。

Abstract: This paper extends the traditional SIS model with birth and death to a directed scale-free network, calculates the endemic equilibrium point and critical epidemic threshold of the model under con-stant and linear node’s infectivity, and puts three traditional immunization schemes on the model, which rigorously proved that under the three immunization strategies, the model’s inhibition of infectious diseases increased. Further comparing the performance of three different immunization strategies under the same average immunization rate, the target immunization of immunizing nodes with large in-degrees and out-degrees is more effective than proportional and acquaintance immunization.