传染病在多层星型耦合网络上的资源控制

doi:10.11772/j.issn.1001-9081.2021030491

《计算机应用》唯一官方网站 ›› 2022, Vol. 42 ›› Issue (5): 1547-1553.DOI: 10.11772/j.issn.1001-9081.2021030491

传染病在多层星型耦合网络上的资源控制

张斯¹, 张必山¹(), 马忠军²

^1.桂林电子科技大学数学与计算科学学院, 广西桂林 541004
^2.广西密码学与信息安全重点实验室(桂林电子科技大学), 广西桂林 541004

收稿日期:2021-03-31 修回日期:2021-07-15 接受日期:2021-07-15 发布日期:2022-06-11 出版日期:2022-05-10
通讯作者: 张必山
作者简介:张斯（1994—），女，四川达州人，硕士研究生，主要研究方向：复杂网络上的传播动力学
张必山（1969—），男，四川达州人，副教授，硕士，主要研究方向：复杂网络上的传播动力学 bshzhang30@sina.com
马忠军（1973—），男，湖南隆回人，教授，博士，主要研究方向：复杂网络上的群体动力学。
基金资助:
广西科技计划项目(桂科AD20297006);广西密码学与信息安全重点实验室研究课题(GCIS202129)

Resource control of infectious disease in multi-layer star coupling network

Si ZHANG¹, Bishan ZHANG¹(), Zhongjun MA²

^1.College of Mathematics and Computing Science，Guilin University of Electronic Technology，Guilin Guangxi 541004，China
^2.Guangxi Key Laboratory of Cryptography and Information Security （Guilin University of Electronic Technology），Guilin Guangxi 541004，China

Received:2021-03-31 Revised:2021-07-15 Accepted:2021-07-15 Online:2022-06-11 Published:2022-05-10
Contact: Bishan ZHANG
About author:ZHANG Si， born in 1994，M. S. candidate. Her research interestsinclude propagation dynamics on complex networks.
ZHANG Bishan， born in 1969，M. S.，associate professor. Hisresearch interests include propagation dynamics on complex networks.
MA Zhongjun， born in 1973，Ph. D.，professor. His researchinterests include group dynamics on complex networks.
Supported by:
Guangxi Science and Technology Program(Guike AD20297006);Research Project of Guangxi Key Laboratory of Cryptography and Information Security(GCIS202129)

摘要/Abstract

摘要：

针对已有传染病传播模型没有考虑到具体的特殊网络结构与资源因素对控制疫情爆发的影响与作用机制，结合双层星型耦合网络与传染病SIS模型，建立了一个离散动态传播模型。该模型利用星型网络的结构特性与平均度概念推导各层感染人口比例关于资源及各种参数的离散方程。理论分析和仿真实验结果表明，多层星型耦合传染病传播网络中存在资源阈值，当节点为叶子节点时，网络存在两个资源阈值，增加资源量投入以抑制传染病传播只在两个资源阈值间有效，此时传染病感染人口比例随着投入资源的增加而减少；当节点为中心节点时，网络中的资源阈值随其他层感染人口比例的增大由两个减少至一个。此外，层间中心节点耦合强度、层间叶子节点耦合强度对疫情的控制效果随着节点所处位置的不同而不同。

关键词: 多层网络, 资源控制, 传染病, SIS模型, 星型网络

Abstract:

Concerning that the existing infectious disease spread model do not consider the influence and mechanism of specific special network structure and resource factors on controlling infectious disease outbreak， a discrete dynamic propagation model was established by combining the two-layer star coupling network with the Susceptible-Infected-Susceptible （SIS） model of infectious disease. In this model， the structural characteristics and the concept of average degree of the star network were used to derive the discrete equations of the proportion of infected population in every layer with resources and various parameters. Theory analysis and simulation experimental results indicate that， the multi-layer star coupling infectious disease spread network has resource thresholds. When the node is a leaf node， the network has two resource thresholds. Increasing the number of resources to control the spread of infectious diseases is only effective between the two resource thresholds. At this time， the proportion of population infected with infectious diseases decreases with the increase of resources invested. When the node is a central node， the resource threshold in the network reduces from two to one with the increase of proportion of infected population in other layers. Additionally， the control effect of the coupling strength of the inter-layer central node and the inter-layer leaf node on the epidemic varies with the location of the nodes.

Key words: multi-layer network, resource control, infectious disease, Susceptible-Infected-Susceptible (SIS) model, star network

中图分类号:

TP391.9

张斯, 张必山, 马忠军. 传染病在多层星型耦合网络上的资源控制[J]. 计算机应用, 2022, 42(5): 1547-1553.

Si ZHANG, Bishan ZHANG, Zhongjun MA. Resource control of infectious disease in multi-layer star coupling network[J]. Journal of Computer Applications, 2022, 42(5): 1547-1553.

图/表 7

图1 双层星型传染病传播耦合网络

Fig. 1 Two-layer star coupling network of infectious disease spread

图2 ρ1随ρ2的演化趋势（i为叶子节点）

Fig. 2 Trend of ρ1 varying with ρ2 （i is the leaf node）

图3 不同ρ2时ρ1随α的演化趋势（i为叶子节点）

Fig. 3 Trend of ρ1 varying with α when ρ2 is different （i is the leaf node）

图4 不同ρ2时ρ1随ω的演化趋势（i为叶子节点）

Fig. 4 Trend of ρ1 varying with ω when ρ2 is different （i is the leaf node）

图5 ρ1随ρ2的演化趋势（i为中心节点）

Fig. 5 Trend of ρ1 varying with ρ2 （i is the central node）

图6 不同ρ2时ρ1随α的演化趋势（i为中心节点）

Fig. 6 Trend of ρ1 varying with α when ρ2 is different （i is the central node）

图7 不同ρ2时ρ1随ω的演化趋势（i为中心节点）

Fig. 7 Trend of ρ1 varying with ω when ρ2 is different （i is the central node）

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传染病在多层星型耦合网络上的资源控制

Resource control of infectious disease in multi-layer star coupling network

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