A unified complete-data likelihood framework for epidemic processes evolving on partially observed dynamic networks that 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.
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.
Inference for epidemic transmission on dynamic networks is fundamentally limited by latent infection times, incomplete contact histories, imperfect observation, and external sources of infection. Although coherent likelihood formulations are available for partially observed epidemic processes, considerably less is known about the theoretical limits of statistical inference under such observation mechanisms. This paper develops a unified framework for studying identifiability and Fisher information in epidemic transmission models observed on dynamic contact networks. We establish conditions for structural and local identifiability, derive observed and complete-data information matrices, and quantify information loss arising from unobserved transmission events and missing network information through a missing-information decomposition. We further investigate how observation frequency, network coverage, and measurement accuracy influence parameter estimability and statistical efficiency, providing a principled basis for evaluating surveillance strategies. Simulation studies demonstrate that the proposed framework accurately characterises the relationship between observation design, statistical information, and parameter estimation, with theoretical predictions closely matching finite-sample performance. The proposed framework clarifies the relationship between observation design, identifiability, and inferential precision, and provides a theoretical foundation for statistical inference in partially observed epidemic transmission models.
We develop an exact finite-population stochastic framework for SIR epidemics evolving under Markovian switching between intervention regimes. The epidemic state is augmented by a finite phase component, allowing transmission, recovery, and direct immunity-acquisition rates to depend on the active regime. Phase-transition intensities may depend on the current epidemic state, so that policy escalation can react to the number of infectious individuals. Exploiting the monotonicity of the susceptible compartment, we derive level-wise recursions for the joint Laplace--Stieltjes transform and probability generating function of the extinction time and the number of infections generated before extinction. These recursions yield the infection-count distribution, conditional extinction-time transforms, and mixed moments linking epidemic duration and infection burden, while replacing a large global linear system with small phase-level solves. The framework is illustrated using weekly mpox incidence data from Luxembourg. A baseline one-phase SIR model is calibrated by maximum likelihood under a Poisson observation model. The calibrated baseline is then used for conditional comparisons of fixed control regimes, early versus delayed strict intervention, vaccination-supported control, and state-dependent escalation. The results show how switching mechanisms affect both the total number of infected individuals and the extinction time, including their dispersion. Since the switching mechanisms are specified rather than estimated from the intervention history, the results are conditional model-based comparisons rather than estimates of the historical effects of interventions in Luxembourg.
Vasileios E. Papageorgiou, Irène Votsi, Samis Trevezas· 0 citations
Identifying asymptomatic individuals (i.e., infected individuals who have no clear symptoms) during epidemic outbreaks is a critical challenge, as they can transmit the disease while remaining undetected. We address this problem using a network-based susceptible–infected–susceptible (SIS) probabilistic epidemic model, where only infected and symptomatic nodes are observable at any given time instant (i.e., an epidemic snapshot). We consider the observation of multiple snapshots, with a parameter that determines the inter-observation time interval. In order to identify the asymptomatic nodes, we introduce cumulative observed betweenness (COB), an extension of observed betweenness centrality that aggregates information across multiple snapshots. When evaluated against baseline methods across diverse network models and epidemic scenarios, COB consistently achieves higher precision, which improves monotonically with the number of snapshots. We further show that the interval between observations strongly affects performance, with widely spaced snapshots providing more informative data. These results demonstrate the potential of network-based inference for identifying asymptomatic individuals under limited testing resources.
C. C. Pinto, Vitor Martins Gouvêa, D. R. Figueiredo· Anais do XXV Workshop em Des...· 0 citations
This work proposes a general framework for model selection in binary-state spreading processes on networks and shows that asymptotic approximations in the thermodynamic limit can accurately predict inference outcomes in finite systems.
Javier Ureña-Carrión, Tiago P. Peixoto, G. Íñiguez· 0 citations
Human mobility plays a central role in shaping contact patterns that drive infectious disease transmission, yet mobility is often simplified in agent-based models (ABMs) due to data and computational constraints. The effects of these simplifications on model outputs are poorly understood. In this study, we systematically examined how alternative mobility assumptions influence emergent contact networks and epidemic dynamics within a large-scale ABM. Using a synthetic population of one million agents representing an urban environment, we implemented five mobility models varying along two dimensions: activity patterns (empirically derived vs. randomized) and destination choice mechanisms (empirical popularity, distance-based, or random). Holding disease parameters constant, we found that mobility assumptions alone produced substantially different contact network structures and epidemic trajectories, including differences in peak incidence and shifts in outbreak timing. Importantly, these differences could not be attributed to agents simply moving more or less overall since aggregate movement volumes were broadly comparable across models. Instead, the contrasting dynamics arose from how mobility generates contact opportunities: specifically, who meets whom, where, and how often. These results suggest that in models where mobility has not been carefully calibrated, simulated epidemic outcomes and evaluations of interventions may reflect mobility assumptions as much as underlying disease parameters. Our findings underscore the importance of mobility model calibration and validation, particularly in policy-facing applications.
K. S. Atwal, Emma Von Hoene, Hossein Amiri et al.· 0 citations
We conduct a retrospective analysis of COVID-19 transmission dynamics across U.S. states using a modified population-based Susceptible-Exposed-Infectious-Asymptomatic-Recovered-Deceased (SEIARD) compartmental model. The proposed framework introduces time-varying transmission, reporting, and mortality rates to capture temporal variations in public behavior and policy interventions during the pandemic. In particular, the transmission rate is modeled as a function of population mobility (derived from Google Mobility Reports), with a residual time-decay term capturing the net effect of unobserved factors such as behavioral adaptation and control measures, while reporting is linked to nationwide testing strategies. We employ a Bayesian approach to integrate multiple data sources and quantify uncertainties in model parameters. The model explicitly distinguishes between symptomatic and asymptomatic infectious individuals and links the latent epidemic states to observable quantities, including reported cases and deaths, through a dynamic reporting function. This retrospective modeling framework provides insights into state-level epidemic trajectories and supports data-driven decision-making for optimal allocation of healthcare resources and evaluation of public health interventions during future pandemics. We further apply a clustering analysis to the posterior parameter estimates to identify groups of U.S. states exhibiting similar epidemiological characteristics, revealing substantial regional heterogeneity in transmission intensity, reproduction dynamics, and mortality burden.
