Accurate identification of the epidemic source is crucial for controlling the spread of infectious disease. During the spread of an epidemic, transmission occurs through the edges, which represent the contact relationship between individuals. Source detection, as a reverse problem, should be significantly benefited by leveraging the epidemic state of edges, as it entails both the direction of transmission and the likelihood of disease spreading through the edges. Although Graph Neural Network (GNN)-based methods have been developed for source detection, their performance is limited due to overlooking the epidemic state of edges. Here, we propose a novel GNN-based model, Adaptive Node and Edge Co-evolution Source Detection graph neural network (ANEC-SD), which utilizes the epidemic state of edges and optimizes the node representations individually to enhance prediction performance. In specific, the ANEC-SD consists of two innovative components, where the Co-evolution of Node and Edge Representations Layer is designed to refine the message aggregation mechanism for effectively characterizing the heterogeneous impact from a node to its neighbors by leveraging the epidemic state of edges. While the Propagation Controller determines the optimal number of propagation layers for each node according to node centrality within the infected subgraph, thereby mitigating the issue of over-smoothing. Experiments on six real-world networks demonstrate that our model significantly outperforms existing methods, achieving a 30% improvement on four out of six networks. Further analysis highlights the pivotal role of epidemic state of edges in message passing.

Monitoring the spread of infectious disease is essential to design and adjust the interventions timely for the prevention of the epidemic outbreak and safeguarding the public health. The governments have generally adopted the incidence-based statistical method to estimate the time-varying effective reproduction number Rt and evaluate the transmission ability of epidemics. However, this method exhibits biases arising from the reported incidence data and assumes the generation interval distribution which is not available at the early stage of epidemic. Recent studies showed that the viral loads characterized by cycle threshold (Ct) of the infected populations evolving throughout the course of epidemic and providing a possibility to infer the epidemic trajectory. In this work, we propose the Cycle Threshold-based Transformer (Ct-Transformer) to estimate Rt. We find the supervised learning of Ct-Transformer outperforms the traditional incidence-based statistic and Ct-based Rt estimating methods, and more importantly Ct-Transformer is robust to the detection resources. Further, we apply the proposed model to self-supervised pre-training tasks and obtain excellent fine-tuned performance, which attains comparable performance with the supervised Ct-Transformer, verified by both the synthetic and real-world datasets. We demonstrate that the Ct-based deep learning method can improve the real-time estimates of Rt, enabling more easily adapted to the track of the newly emerged epidemic.

Many network analysis tasks like classification over nodes require careful efforts in engineering features used by learning algorithms. Most of recent studies have been made and succeeded in the field of static network representation learning. However, real-world networks are often dynamic and little work has been done on how to describe dynamic networks. In this work, we pose the problem of condensing dynamic networks and introduce SuRep, an encoding-decoding framework which utilizes matrix factorization technique to derive a succinct representation of a dynamic network in any stationary phase. We show that the succinct representation method can uncover the invariant structural properties in the network evolution and derive dense feature representations of the nodes as the byproduct. This method can be easily extended to dynamic attribute networks. For experiments on detecting change points in dynamic networks and network classification with real-world datasets we demonstrate SuRep's potential for capturing latent patterns among nodes.