Epidemic prediction is of practical significance in public health, enabling early intervention, resource allocation, and strategic planning. However, privacy concerns often hinder the sharing of health data among institutions, limiting the development of accurate prediction models. In this paper, we develop a general privacy-preserving framework for node-level epidemic prediction on networks based on federated learning (FL). We frame the spatio-temporal spread of epidemics across multiple data-isolated subnetworks, where each node state represents the aggregate epidemic severity within a community. Then, both the pure temporal LSTM model and the spatio-temporal model i.e., Spatio-Temporal Graph Attention Network (STGAT) are proposed to address the federated epidemic prediction. Extensive experiments are conducted on various epidemic processes using a practical airline network, offering a comprehensive assessment of FL efficacy under diverse scenarios. By introducing the efficacy energy metric to measure system robustness under various client configurations, we systematically explore key factors influencing FL performance, including client numbers, aggregation strategies, graph partitioning, missing infectious reports. Numerical results manifest that STGAT excels in capturing spatio-temporal dependencies in dynamic processes whereas LSTM performs well in simpler pattern. Moreover, our findings highlight the importance of balancing feature consistency and volume uniformity among clients, as well as the prediction dilemma between information richness and intrinsic stochasticity of dynamic processes. This study offers practical insights into the efficacy of FL scenario in epidemic management, demonstrates the potential of FL to address broader collective dynamics.

Computing observables from conditioned dynamics is typically computationally hard, because, although obtaining independent samples efficiently from the unconditioned dynamics is usually feasible, generally most of the samples must be discarded (in a form of importance sampling) because they do not satisfy the imposed conditions. Sampling directly from the conditioned distribution is non-trivial, as conditioning breaks the causal properties of the dynamics which ultimately renders the sampling procedure efficient. One standard way of achieving it is through a Metropolis Monte-Carlo procedure, but this procedure is normally slow and a very large number of Monte-Carlo steps is needed to obtain a small number of statistically independent samples. In this work, we propose an alternative method to produce independent samples from a conditioned distribution. The method learns the parameters of a generalized dynamical model that optimally describe the conditioned distribution in a variational sense. The outcome is an effective, unconditioned, dynamical model, from which one can trivially obtain independent samples, effectively restoring causality of the conditioned distribution. The consequences are twofold: on the one hand, it allows us to efficiently compute observables from the conditioned dynamics by simply averaging over independent samples. On the other hand, the method gives an effective unconditioned distribution which is easier to interpret. The method is flexible and can be applied virtually to any dynamics. We discuss an important application of the method, namely the problem of epidemic risk assessment from (imperfect) clinical tests, for a large family of time-continuous epidemic models endowed with a Gillespie-like sampler. We show that the method compares favorably against the state of the art, including the soft-margin approach and mean-field methods.

Reconstructing missing information in epidemic spreading on contact networks can be essential in prevention and containment strategies. For instance, identifying and warning infective but asymptomatic individuals (e.g., manual contact tracing) helped contain outbreaks in the COVID-19 pandemic. The number of possible epidemic cascades typically grows exponentially with the number of individuals involved. The challenge posed by inference problems in the epidemics processes originates from the difficulty of identifying the almost negligible subset of those compatible with the evidence (for instance, medical tests). Here we present a new generative neural networks framework that can sample the most probable infection cascades compatible with observations. Moreover, the framework can infer the parameters governing the spreading of infections. The proposed method obtains better or comparable results with existing methods on the patient zero problem, risk assessment, and inference of infectious parameters in synthetic and real case scenarios like spreading infections in workplaces and hospitals.

We approach the development of models and control strategies of susceptible-infected-susceptible (SIS) epidemic processes from the perspective of marked temporal point processes and stochastic optimal control of stochastic differential equations (SDEs) with jumps. In contrast to previous work, this novel perspective is particularly well-suited to make use of fine-grained data about disease outbreaks, and it lets us overcome the shortcomings of current control strategies. Our control strategy resorts to treatment intensities to determine who to treat and when to do so, to minimize the amount of infected individuals over time. Preliminary experiments with synthetic data show that our control strategy consistently outperforms several alternatives. Looking into the future, we believe our methodology provides a promising step towards the development of practical data-driven control strategies of epidemic processes.