Inferring stochastic dynamics from incomplete observations of network spreading processes

Inferring the dynamics of infectious diseases enables prediction and intervention. During early monitoring, available information may comprise digital contact data that partly resolve the interaction network and intermittent screening data that leave the states of some nodes unresolved. Learning-based methods can introduce further information loss by compressing available network and state information into summary statistics. To retain the correspondence between node states and network positions, we develop Graph-Sequence Transformer Attention (GTA), which uses observed node states, network topology, and observation times to infer infection and recovery probabilities for susceptible-infectious-recovered spreading. We compare GTA with summary-based XGBoost and a one-dimensional convolutional neural network and with maximum-likelihood estimation of the recovery probability. Across four synthetic network classes and five empirical topologies, the three learning methods often perform comparably and respond similarly to changes in network size, mean degree, and observation timing. GTA is usually most accurate for estimating infection on sparse, heterogeneous networks, whereas summary-based methods often match or outperform it on denser, more homogeneous networks. For a fixed number of observations, wider spacing can initially improve inference by covering more of the spreading trajectory, but eventually increases error as intermediate transitions are missed. Maximum-likelihood estimation can outperform learning methods when recovery transitions are well resolved, but deteriorates as observations become more widely separated. Losing information about node states can compromise performance more than losing information about edges. Overall, the results show how inference from incomplete observations depends on network structure, temporal sampling, and the information retained in the observations.