Ensemble inference of unobserved infections in networks using partial observations

Undetected infections fuel the dissemination of many infectious agents. However, identification of unobserved infectious individuals remains challenging due to limited observations of infections and imperfect knowledge of key transmission parameters. Here, we use an ensemble Bayesian inference method to infer unobserved infections using partial observations. The ensemble inference method can represent uncertainty in model parameters and update model states using all ensemble members collectively. We perform extensive experiments in both model-generated and real-world networks in which individuals have differential but unknown transmission rates. The ensemble method outperforms several alternative approaches for a variety of network structures and observation rates, despite that the model is mis-specified. Additionally, the computational complexity of this algorithm scales almost linearly with the number of nodes in the network and the number of observations, respectively, exhibiting the potential to apply to large-scale networks. The inference method may support decision-making under uncertainty and be adapted for use for other dynamical models in networks.Author summary: Mathematical models in networks can be used to infer unobserved infections and support decision-making in outbreak control and management. However, a major challenge in the operational use of these models is model misspecification–whether models can reliably represent the real-world disease transmission process. As we can only observe part of the transmission process, mathematical models are inherently misspecified due to the uncertainty in the model structure and parameters. A reliable modeling method, therefore, should be robust to such uncertainty and imperfect knowledge of the transmission dynamics to support real-time decision-making. In this study, we used an ensemble inference method to infer unobserved infections using partial observations. We considered the condition where individuals have differential but unknown transmission rates as an example of model uncertainty mirroring the situation encountered in real-world settings. We found the ensemble inference can robustly infer unobserved infections using partial observations with uncertainty in model parameters, although the distribution of parameters is mis-specified. The ensemble inference algorithm presents a general framework for inference of spreading dynamics in networks and may contribute to the toolbox supporting operational epidemic control in the face of model uncertainty and limited observation.