This paper presents a comprehensive review of Graph Neural Networks (GNNs) in epidemic modeling, highlighting their potential in addressing limitations of traditional mechanistic models. The authors introduce hierarchical taxonomies for epidemic tasks and methodologies, offering a trajectory of development in this domain. For epidemic tasks, they establish a taxonomy akin to those typically employed within the epidemic domain. For methodology, they categorize existing work into Neural Models and Hybrid Models. The paper provides an exhaustive and systematic examination of these methodologies, encompassing both the tasks and their technical details. It also discusses the limitations of existing methods from diverse perspectives and systematically proposes future research directions. The survey aims to bridge literature gaps and promote the progression of this promising field. The authors hope that it will facilitate synergies between the communities of GNNs and epidemiology, and contribute to their collective progress. The paper includes a detailed overview of related surveys and provides a comprehensive review of GNNs in epidemic modeling, including their applications in infection prediction, outbreak source detection, and intervention modeling. The authors also discuss the importance of data sources, such as demographic and health records, mobility information, online search and social media, sensors, and simulated data, in epidemic modeling. They provide a taxonomy for graph construction based on the dynamicity of nodes and edges, and discuss methodological distinctions between Neural Models and Hybrid Models. The paper concludes with a detailed illustration of the methods in epidemic modeling, divided into Neural Models and Hybrid Models, and discusses their applications in spatial dynamics modeling, temporal dynamics modeling, and intervention modeling. The authors also highlight the importance of integrating mechanistic models with neural networks to enhance the accuracy and interpretability of disease forecasting. The paper provides a detailed analysis of various GNN-based methods and their applications in epidemic modeling, emphasizing their potential in capturing complex relational information and improving the accuracy of predictions. The authors also discuss the challenges and limitations of existing methods and propose future research directions for the field. The paper is a valuable resource for researchers interested in the intersection of GNNs and epidemiology, offering a comprehensive overview of the current state of research and future directions.This paper presents a comprehensive review of Graph Neural Networks (GNNs) in epidemic modeling, highlighting their potential in addressing limitations of traditional mechanistic models. The authors introduce hierarchical taxonomies for epidemic tasks and methodologies, offering a trajectory of development in this domain. For epidemic tasks, they establish a taxonomy akin to those typically employed within the epidemic domain. For methodology, they categorize existing work into Neural Models and Hybrid Models. The paper provides an exhaustive and systematic examination of these methodologies, encompassing both the tasks and their technical details. It also discusses the limitations of existing methods from diverse perspectives and systematically proposes future research directions. The survey aims to bridge literature gaps and promote the progression of this promising field. The authors hope that it will facilitate synergies between the communities of GNNs and epidemiology, and contribute to their collective progress. The paper includes a detailed overview of related surveys and provides a comprehensive review of GNNs in epidemic modeling, including their applications in infection prediction, outbreak source detection, and intervention modeling. The authors also discuss the importance of data sources, such as demographic and health records, mobility information, online search and social media, sensors, and simulated data, in epidemic modeling. They provide a taxonomy for graph construction based on the dynamicity of nodes and edges, and discuss methodological distinctions between Neural Models and Hybrid Models. The paper concludes with a detailed illustration of the methods in epidemic modeling, divided into Neural Models and Hybrid Models, and discusses their applications in spatial dynamics modeling, temporal dynamics modeling, and intervention modeling. The authors also highlight the importance of integrating mechanistic models with neural networks to enhance the accuracy and interpretability of disease forecasting. The paper provides a detailed analysis of various GNN-based methods and their applications in epidemic modeling, emphasizing their potential in capturing complex relational information and improving the accuracy of predictions. The authors also discuss the challenges and limitations of existing methods and propose future research directions for the field. The paper is a valuable resource for researchers interested in the intersection of GNNs and epidemiology, offering a comprehensive overview of the current state of research and future directions.