有限资源限制下双层网络间的传染病传播模型研究

Research on the Epidemic Spreading Model between Two-Layer Networks under the Constraint of Limited Resources

摘要: 因人们在社会中的不同角色的关系而会有不同的网络连接方式，网络结构对传染病的扩散也有重要的影响，特别是近几年来，双层网络在传染病模型中被广泛运用。基于此，本文开展有限资源限制下的双层网络间的传染病传播模型研究，其中一层是信息传播层，另一层是疾病传播层，两层的节点代表相同的实体，但两层节点的连接方式不同。本文提出了双层网络上的UAU-SIS信息–疾病传播动力学模型，并创新的引入资源函数μ，μ的数值是随着资源量和双层网络中被感染者人数的变化而变化的。通过马尔科夫链的方法求出了疾病传播的阈值，并发现在合理的区间控制资源量对传染病的遏制具有影响。

Abstract: Due to the different roles of people in society, there are different network connection modes, and the network structure also has an important impact on the spread of infectious diseases. In recent years, especially, the two-layer network has been widely used in infectious disease models. Based on this, this paper studies the infectious disease spreading model between two-layer networks under the restriction of limited resources. One layer is the information dissemination layer, and the other layer is the disease dissemination layer. The nodes on both layers represent the same entity, but the connection mode of nodes on both layers is different. This paper proposes a UAU-SIS information-disease spreading dynamics model on the two-layer network, and innovatively introduces a resource function μ, whose value changes with the amount of resources and the number of infected people in the two-layer network. The threshold value of disease transmission is obtained by Markov chain method, and it is found that controlling the amount of resources within a reasonable range has an impact on the containment of infectious diseases.