Advancing epidemic dynamics forecasting is vital for targeted interventions and safeguarding public health. Current approaches mainly fall into two categories: mechanism-based and data-driven models. Mechanism-based models are constrained by predefined compartmental structures and oversimplified system assumptions, limiting their ability to model complex real-world dynamics, while data-driven models focus solely on intrinsic data dependencies without physical or epidemiological constraints, risking biased or misleading representations. Although recent studies have attempted to integrate epidemiological knowledge into neural architectures, most of them fail to reconcile explicit physical priors with neural representations. To overcome these obstacles, we introduce Epi$^2$-Net, a Epidemic Forecasting Framework built upon Physics-Inspired Neural Networks. Specifically, we propose reconceptualizing epidemic transmission from the physical transport perspective, introducing the concept of neural epidemic transport. Further, we present a physic-inspired deep learning framework, and integrate physical constraints with neural modules to model spatio-temporal patterns of epidemic dynamics. Experiments on real-world datasets have demonstrated that Epi$^2$-Net outperforms state-of-the-art methods in epidemic forecasting, providing a promising solution for future epidemic containment. The code is available at: https://anonymous.4open.science/r/Epi-2-Net-48CE.

Advanced epidemic forecasting is critical for enabling precision containment strategies, highlighting its strategic importance for public health security. While recent advances in Large Language Models (LLMs) have demonstrated effectiveness as foundation models for domain-specific tasks, their potential for epidemic forecasting remains largely unexplored. In this paper, we introduce EpiLLM, a novel LLM-based framework tailored for spatio-temporal epidemic forecasting. Considering the key factors in real-world epidemic transmission: infection cases and human mobility, we introduce a dual-branch architecture to achieve fine-grained token-level alignment between such complex epidemic patterns and language tokens for LLM adaptation. To unleash the multi-step forecasting and generalization potential of LLM architectures, we propose an autoregressive modeling paradigm that reformulates the epidemic forecasting task into next-token prediction. To further enhance LLM perception of epidemics, we introduce spatio-temporal prompt learning techniques, which strengthen forecasting capabilities from a data-driven perspective. Extensive experiments show that EpiLLM significantly outperforms existing baselines on real-world COVID-19 datasets and exhibits scaling behavior characteristic of LLMs.

Accurate epidemic forecasting is crucial for effective disease control and prevention. Traditional compartmental models often struggle to estimate temporally and spatially varying epidemiological parameters, while deep learning models typically overlook disease transmission dynamics and lack interpretability in the epidemiological context. To address these limitations, we propose a novel Causal Spatiotemporal Graph Neural Network (CSTGNN), a hybrid framework that integrates a Spatio-Contact SIR model with Graph Neural Networks (GNNs) to capture the spatiotemporal propagation of epidemics. Inter-regional human mobility exhibits continuous and smooth spatiotemporal patterns, leading to adjacent graph structures that share underlying mobility dynamics. To model these dynamics, we employ an adaptive static connectivity graph to represent the stable components of human mobility and utilize a temporal dynamics model to capture fluctuations within these patterns. By integrating the adaptive static connectivity graph with the temporal dynamics graph, we construct a dynamic graph that encapsulates the comprehensive properties of human mobility networks. Additionally, to capture temporal trends and variations in infectious disease spread, we introduce a temporal decomposition model to handle temporal dependence. This model is then integrated with a dynamic graph convolutional network for epidemic forecasting. We validate our model using real-world datasets at the provincial level in China and the state level in Germany. Extensive studies demonstrate that our method effectively models the spatiotemporal dynamics of infectious diseases, providing a valuable tool for forecasting and intervention strategies. Furthermore, analysis of the learned parameters offers insights into disease transmission mechanisms, enhancing the interpretability and practical applicability of our model.

Accurate forecasting of epidemic infection trajectories is crucial for safeguarding public health. However, limited data availability during emerging outbreaks and the complex interaction between environmental factors and disease dynamics present significant challenges for effective forecasting. In response, we introduce CAPE, a novel epidemic pre-training framework designed to harness extensive disease datasets from diverse regions and integrate environmental factors directly into the modeling process for more informed decision-making on downstream diseases. Based on a covariate adjustment framework, CAPE utilizes pre-training combined with hierarchical environment contrasting to identify universal patterns across diseases while estimating latent environmental influences. We have compiled a diverse collection of epidemic time series datasets and validated the effectiveness of CAPE under various evaluation scenarios, including full-shot, few-shot, zero-shot, cross-location, and cross-disease settings, where it outperforms the leading baseline by an average of 9.9% in full-shot and 14.3% in zero-shot settings. The code will be released upon acceptance.

Accurate and trustworthy epidemic forecasting is an important problem for public health planning and disease mitigation. Recent works in deep neural models for uncertainty-aware time-series forecasting also have several limitations; e.g., it is difficult to specify proper priors in Bayesian NNs, while methods like deep ensembling can be computationally expensive. In this paper, we propose to use neural functional processes to fill this gap. We model epidemic time-series with a probabilistic generative process and propose a functional neural process model called EpiFNP, which directly models the probability distribution of the forecast value in a non-parametric way. In EpiFNP, we use a dynamic stochastic correlation graph to model the correlations between sequences, and design different stochastic latent variables to capture functional uncertainty from different perspectives.

Among various spatio-temporal prediction tasks, epidemic forecasting plays a critical role in public health management. Recent studies have demonstrated the strong potential of spatio-temporal graph neural networks (STGNNs) in extracting heterogeneous spatio-temporal patterns for epidemic forecasting. However, most of these methods bear an over-simplified assumption that two locations (e.g., cities) with similar observed features in previous time steps will develop similar infection numbers in the future. In fact, for any epidemic disease, there exists strong heterogeneity of its intrinsic evolution mechanisms across geolocation and time, which can eventually lead to diverged infection numbers in two ``similar'' locations. However, such mechanistic heterogeneity is non-trivial to be captured due to the existence of numerous influencing factors like medical resource accessibility, virus mutations, mobility patterns, etc., most of which are spatio-temporal yet unreachable or even unobservable. To address this challenge, we propose a Heterogeneous Epidemic-Aware Transmission Graph Neural Network (HeatGNN), a novel epidemic forecasting framework. By binding the epidemiology mechanistic model into a GNN, HeatGNN learns epidemiology-informed location embeddings of different locations that reflect their own transmission mechanisms over time. With the time-varying mechanistic affinity graphs computed with the epidemiology-informed location embeddings, a heterogeneous transmission graph network is designed to encode the mechanistic heterogeneity among locations, providing additional predictive signals to facilitate accurate forecasting. Experiments on three benchmark datasets have revealed that HeatGNN outperforms various strong baselines. Moreover, our efficiency analysis verifies the real-world practicality of HeatGNN on datasets of different sizes.

Forecasting temporal processes such as virus spreading in epidemics often requires more than just observed time-series data, especially at the beginning of a wave when data is limited. Traditional methods employ mechanistic models like the SIR family, which make strong assumptions about the underlying spreading process, often represented as a small set of compact differential equations. Data-driven methods such as deep neural networks make no such assumptions and can capture the generative process in more detail, but fail in long-term forecasting due to data limitations. We propose a new hybrid method called MP-PINN (Multi-Phase Physics-Informed Neural Network) to overcome the limitations of these two major approaches. MP-PINN instils the spreading mechanism into a neural network, enabling the mechanism to update in phases over time, reflecting the dynamics of the epidemics due to policy interventions. Experiments on COVID-19 waves demonstrate that MP-PINN achieves superior performance over pure data-driven or model-driven approaches for both short-term and long-term forecasting.

Accurate epidemic forecasting is a critical task in controlling disease transmission. Many deep learning-based models focus only on static or dynamic graphs when constructing spatial information, ignoring their relationship. Additionally, these models often rely on recurrent structures, which can lead to error accumulation and computational time consumption. To address the aforementioned problems, we propose a novel model called Backbone-based Dynamic Graph Spatio-Temporal Network (BDGSTN). Intuitively, the continuous and smooth changes in graph structure, make adjacent graph structures share a basic pattern. To capture this property, we use adaptive methods to generate static backbone graphs containing the primary information and temporal models to generate dynamic temporal graphs of epidemic data, fusing them to generate a backbone-based dynamic graph. To overcome potential limitations associated with recurrent structures, we introduce a linear model DLinear to handle temporal dependencies and combine it with dynamic graph convolution for epidemic forecasting. Extensive experiments on two datasets demonstrate that BDGSTN outperforms baseline models and ablation comparison further verifies the effectiveness of model components. Furthermore, we analyze and measure the significance of backbone and temporal graphs by using information metrics from different aspects. Finally, we compare model parameter volume and training time to confirm the superior complexity and efficiency of BDGSTN.

Infectious disease forecasting has been a key focus and proved to be crucial in controlling epidemic. A recent trend is to develop forecast-ing models based on graph neural networks (GNNs). However, existing GNN-based methods suffer from two key limitations: (1) Current models broaden receptive fields by scaling the depth of GNNs, which is insuffi-cient to preserve the semantics of long-range connectivity between distant but epidemic related areas. (2) Previous approaches model epidemics within single spatial scale, while ignoring the multi-scale epidemic pat-terns derived from different scales. To address these deficiencies, we devise the Multi-scale Spatio-temporal Graph Neural Network (MSGNN) based on an innovative multi-scale view. To be specific, in the proposed MSGNN model, we first devise a novel graph learning module, which directly captures long-range connectivity from trans-regional epidemic signals and integrates them into a multi-scale graph. Based on the learned multi-scale graph, we utilize a newly designed graph convolution module to exploit multi-scale epidemic patterns. This module allows us to facilitate multi-scale epidemic modeling by mining both scale-shared and scale-specific pat-terns. Experimental results on forecasting new cases of COVID-19 in United State demonstrate the superiority of our method over state-of-arts. Further analyses and visualization also show that MSGNN offers not only accurate, but also robust and interpretable forecasting result.

Accurate epidemic forecasting plays a vital role for governments in developing effective prevention measures for suppressing epidemics. Most of the present spatio-temporal models cannot provide a general framework for stable, and accurate forecasting of epidemics with diverse evolution trends. Incorporating epidemiological domain knowledge ranging from single-patch to multi-patch into neural networks is expected to improve forecasting accuracy. However, relying solely on single-patch knowledge neglects inter-patch interactions, while constructing multi-patch knowledge is challenging without population mobility data. To address the aforementioned problems, we propose a novel hybrid model called Metapopulation-based Spatio-Temporal Attention Network (MPSTAN). This model aims to improve the accuracy of epidemic forecasting by incorporating multi-patch epidemiological knowledge into a spatio-temporal model and adaptively defining inter-patch interactions. Moreover, we incorporate inter-patch epidemiological knowledge into both the model construction and loss function to help the model learn epidemic transmission dynamics. Extensive experiments conducted on two representative datasets with different epidemiological evolution trends demonstrate that our proposed model outperforms the baselines and provides more accurate and stable short- and long-term forecasting. We confirm the effectiveness of domain knowledge in the learning model and investigate the impact of different ways of integrating domain knowledge on forecasting. We observe that using domain knowledge in both model construction and loss functions leads to more efficient forecasting, and selecting appropriate domain knowledge can improve accuracy further.