A Complete-Data Likelihood for Epidemic Processes on Partially Observed Dynamic Networks
This study addresses the compounded challenges in inferring epidemic spread on partially observed dynamic contact networks—namely, unknown infection times, incomplete network evolution, measurement errors in contacts, and external sources of infection. The authors propose a unified continuous-time stochastic process framework that jointly models SEIR transmission dynamics, state-dependent network evolution, and a symptom-contact observation mechanism. They derive, for the first time, the complete-data event-history likelihood of the coupled epidemic-network process under partial observability, establishing a theoretical foundation for both likelihood-based and Bayesian inference, and demonstrating that existing models arise as special cases. By integrating data augmentation and probabilistic graphical modeling, the approach simultaneously accounts for latent incubation periods, intermittent observations, contact misreporting, and exogenous infection pressure, revealing how disease progression and contact dynamics jointly govern parameter identifiability.