论文标题
使用疫苗接种在地理网络上缓解流行病
Mitigating an epidemic on a geographic network using vaccination
论文作者
论文摘要
我们考虑了一个数学模型，描述了在地理网络上流行病的传播。暴发的大小受疾病的初始生长速度的控制，该疾病的最大特征值由易感基质形成的流行病基质和代表迁移率的图表laplacian形成。我们使用基质扰动理论来分析流行病基质并定义疫苗接种策略，假设疫苗接种减少了易感。当活动能力和局部疾病动态具有相似的时间尺度时，疫苗接种整个网络是最有效的，因为该疾病均匀增长。但是，如果只能接种几个顶点，那么我们选择哪个顶点？我们回答这个问题，并表明沿对应于Laplacian最大特征值的特征向量疫苗是最有效的。我们在7个顶点图和法国铁路网络的现实例子上说明了这些一般结果。当迁移率慢于局部疾病动态时，流行病在顶点上具有最大的易感性。疫苗接种更大的顶点时，流行病的速度会更降低。这也取决于相邻的顶点。这项研究及其结论提供了在流行病开始时在网络上疫苗接种计划的准则。
We consider a mathematical model describing the propagation of an epidemic on a geographical network. The size of the outbreak is governed by the initial growth rate of the disease given by the maximal eigenvalue of the epidemic matrix formed by the susceptibles and the graph Laplacian representing the mobility. We use matrix perturbation theory to analyze the epidemic matrix and define a vaccination strategy, assuming the vaccination reduces the susceptibles. When mobility and local disease dynamics have similar time scales, it is most efficient to vaccinate the whole network because the disease grows uniformly. However, if only a few vertices can be vaccinated then which ones do we choose? We answer this question, and show that it is most efficient to vaccinate along an eigenvector corresponding to the largest eigenvalue of the Laplacian. We illustrate these general results on a 7 vertex graph and a realistic example of the french rail network. When mobility is slower than local disease dynamics, the epidemic grows on the vertex with largest susceptibles. The epidemic growth rate is more reduced when vaccinating a larger degree vertex; it also depends on the neighboring vertices. This study and its conclusions provides guidelines for the planning of vaccination on a network at the onset of an epidemic.
