Deep learning framework for predicting stochastic take-off and die-out of early spreading

TL;DR

The paper tackles early-stage uncertainty in outbreak fate by framing it as a stochastic prediction problem and developing a deep-learning framework that leverages network structure and temporal dynamics. The Outbreak-GWN model fuses GraphWave-based structural embeddings with Bi-GRU temporal learning and an MLP predictor to forecast whether initial transmissions will die out or take off, outperforming baselines across ER and BA networks and multiple infectivity levels. A pretrain-finetune paradigm further enhances cross-domain generalization by learning universal spreading patterns from diverse simulations and fine-tuning on limited, scenario-specific data. The approach offers a practical, real-time tool for epidemic preparedness and extends naturally to other contagion-like processes, with public code and data to enable reproducibility.

Abstract

Large-scale outbreaks of epidemics, misinformation, or other harmful contagions pose significant threats to human society, yet the fundamental question of whether an emerging outbreak will escalate into a major epidemic or naturally die out remains largely unaddressed. This problem is challenging, partially due to inadequate data during the early stages of outbreaks and also because established models focus on average behaviors of large epidemics rather than the stochastic nature of small transmission chains. Here, we introduce the first systematic framework for forecasting whether initial transmission events will amplify into major outbreaks or fade into extinction during early stages, when intervention strategies can still be effectively implemented. Using extensive data from stochastic spreading models, we developed a deep learning framework that predicts early-stage spreading outcomes in real-time. Validation across Erdős-Rényi and Barabási-Albert networks with varying infectivity levels shows our method accurately forecasts stochastic spreading events well before potential outbreaks, demonstrating robust performance across different network structures and infectivity scenarios.To address the challenge of sparse data during early outbreak stages, we further propose a pretrain-finetune framework that leverages diverse simulation data for pretraining and adapts to specific scenarios through targeted fine-tuning. The pretrain-finetune framework consistently outperforms baseline models, achieving superior performance even when trained on limited scenario-specific data. To our knowledge, this work presents the first framework for predicting stochastic take-off versus die-out. This framework provides valuable insights for epidemic preparedness and public health decision-making, enabling more informed early intervention strategies.

Figures (11)

• Figure 1: Dynamics of deterministic and stochastic SIR model. (a) Comparing the dynamics of the deterministic SIR model and the trajectories of 200 stochastic simulation samples. (b) Distribution of final recovered population from 100,000 stochastic simulations. Here, ($M_0$) corresponds to stochastic die-out, while ($M_L$) represents stochastic outbreak.
• Figure 2: Overview of the stochastic outbreak prediction task. (a) Trajectories of a few stochastic simulation samples. (b) Temporal graphs of several observed transmissions. (c) Prediction method. (d) The distribution of die-outs and take-off results from 100,000 stochastic simulations. $\phi*$ represents the threshold value for stochastic die-outs and take-off events. $t_o$ refers to the time observed to predict the outbreak of the spreading.
• Figure 3: The architecture of Outbreak-GWN.
• Figure 4: Stochastic outbreak prediction with medium infectivity scenario in BA network. (a) 100 trajectories simulated with medium infectivity $\beta = 0.02$. (b) The distribution of final recovers of 500000 stochastic simulations with medium infectivity $\beta = 0.02$. (c) Probability of stochastic die-out and take-off. (d) Model performances across varying observation times $T_o$ ranging from 10 to 30.
• Figure 5: Stochastic outbreak prediction with medium infectivity scenario in ER network. (a) 100 trajectories simulated with medium infectivity $\beta = 0.033$. (b) The distribution of final recoveries of 500000 stochastic simulations with medium infectivity $\beta = 0.033$. (c) Probability of stochastic die-out and take-off. (d) Model performances across varying observation times $T_o$ ranging from 28 to 58.