A Complete-Data Likelihood for Epidemic Processes on Partially Observed Dynamic Networks

2026-07-16

AI Summary

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.

Abstract

Inference for infectious disease transmission on dynamic contact networks is complicated by latent infection times, partially observed network evolution, measurement error in contact data, and infection originating from outside the observed population. Existing likelihood-based approaches typically address these challenges separately and often rely on restrictive assumptions such as fully observed networks, closed populations, or symptom onset as a surrogate for infection time. We develop a unified complete-data likelihood framework for epidemic processes evolving on partially observed dynamic networks. The proposed formulation represents disease progression, network evolution, and observation mechanisms as interacting continuous-time stochastic processes within a common probabilistic framework. Specifically, we couple a susceptible-exposed-infectious-removed (SEIR) epidemic process with a status-dependent dynamic contact network and explicit observation models for symptoms and contacts. The resulting framework accommodates latent incubation periods, intermittent network observation, contact measurement error, and external infection pressure while preserving a coherent likelihood structure. Our principal contribution is the derivation of a complete-data event-history likelihood for the joint epidemic-network process under partial observation. The likelihood provides a rigorous foundation for likelihood-based and Bayesian inference through data augmentation, clarifies how information from disease progression and contact dynamics jointly determines parameter estimability, and reveals a broad class of existing epidemic network models as special cases. More generally, the framework contributes to statistical inference for partially observed interacting stochastic systems on evolving networks and establishes a foundation for uncertainty-aware analysis of complex transmission processes.

Problem

• epidemic processes
• partially observed networks
• dynamic contact networks
• latent infection times
• external infection

Innovation

• complete-data likelihood
• dynamic contact networks
• partially observed systems
• SEIR epidemic model
• stochastic process coupling