传染病在多层星型耦合网络上的资源控制

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。

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

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.