CAJ | 학술논문

考虑在有向网络中的流行病阈值以及免疫措施分析的问题,利用SIS模型详细研究了有向网络上的传染病动力学行为.首先获得了一个依赖于有向网络的出度与入度分布和传染力函数的流行病阈值,接着给出了技术网络和社会网络上的流行病阈值表达式.进一步发现当传染力是一个常数时,有向网络中具有较大出度的网络类型更利于疾病传播;而当传染力与网络的出度成正比时,疾病在这两种类型的网络中的传播阈值是相同的.最后通过计算和比较3种在不同的免疫措施下有向网络的流行病阈值,得出了目标免疫明显优于随机免疫和熟人免疫,而随机免疫和熟人免疫的有效性则依赖于网络的入度分布的结论.
고필재유향망락중적류행병역치이급면역조시분석적문제,이용SIS모형상세연구료유향망락상적전염병동역학행위.수선획득료일개의뢰우유향망락적출도여입도분포화전염력함수적류행병역치,접착급출료기술망락화사회망락상적류행병역치표체식.진일보발현당전염력시일개상수시,유향망락중구유교대출도적망락류형경리우질병전파;이당전염력여망락적출도성정비시,질병재저량충류형적망락중적전파역치시상동적.최후통과계산화비교3충재불동적면역조시하유향망락적류행병역치,득출료목표면역명현우우수궤면역화숙인면역,이수궤면역화숙인면역적유효성칙의뢰우망락적입도분포적결론.
We consider the problem of epidemic threshold and immunization strategies analysis in directed networks .In this paper ,we investigate and analyse the epidemic dynamics on directed networks via an SIS model .First ,we give a general expression of the epidemic threshold ,which depends on the in‐degree and out‐degree distributions of the directed network ,and the infectivity function .We figure out the epidemic thresholds on technological and social networks .We find that if the infectivity is a constant ,the network with larger average out‐degree is more conducive to the spread of diseases ,and if the infectivity is proportional to node's out‐degree ,diseases have the same chance to spread in these two kinds of networks .At last ,we compute the epidemic thresholds on directed networks with three different immunization schemes .By comparison ,we find that targeted immunization has clear superiority to proportional and acquaintance immuniza‐tions ,and the validity of proportional and acquaintance immunizations relies on the in‐degree dis‐tribution of networks .