A unified framework for studying identifiability and Fisher information in epidemic transmission models observed on dynamic contact networks is developed, establishing 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.
Abstract
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.
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.
Models incorporating household structure, with different rates of transmission within and between households, are widely used in infectious disease epidemiology. These models can be calibrated using final-size data in which transmission ordering is ignored because it does not affect the distribution of final outbreak sizes. In particular, many distinct transmission histories produce identical final epidemiological outcomes, making it difficult to distinguish internal (within-household) from external (between-household) transmission and limiting parameter identifiability. Here, we develop a continuous-time Markov chain formulation for household transmission dynamics in which the model state space is expanded to include transmission graphs describing infection direction and order, with idealised pathogen genomic data used to identify the transmission histories compatible with observations. We conduct simulation studies which show that incorporating genetic information substantially concentrates the regions of high likelihood compared with models based on epidemiological data alone. In particular, genomic data reduces the dependence between internal and external transmission parameters, removing the characteristic ridge associated with their weak identifiability. These results demonstrate that graph-resolved household models enable improved transmission inference while maintaining analytical and computational tractability.
Public-health surveillance systems rely on downstream indicators to infer latent infection incidence, but delays and observation noise provide only an indirect and temporally distorted view of the underlying epidemic process. Reconstructing upstream epidemic trajectories from these observations is therefore an ill-posed inverse problem, in which different reconstruction assumptions may produce different trajectories that remain consistent with the observed data. Here, we develop a general spectral framework that quantifies the statistical distinguishability of candidate upstream trajectories under delayed and noisy observations. We show that epidemiological delay distributions impose a frequency-dependent temporal resolution limit on epidemic surveillance, fundamentally constraining the distinguishability of rapid upstream variation. This limitation propagates to epidemiological inference, making some quantities substantially more sensitive to reconstruction assumptions than others and rendering distinct event-impact profiles difficult to distinguish from downstream observations.
J. Tang, B. Wilder, R. Rosenfeld· medRxiv· 0 citations
Experiments with synthetic data and COVID-19 surveillance data show that SUC–PINN recovers plausible hidden infection trajectories, yields stable parameter estimates, and provides accurate short-term forecasts, support SUC–PINN as a practical computational approach for inverse modeling and prediction in partially observed epidemic dynamics.
U. M. Rifanti, N. Susyanto, Ratinan Boonklurb· Advances in Complex Systems· 0 citations
Early epidemic control often relies on case-finding operations. To assess their theoretical efficacy, we develop an infection-age structured early growth transmission model that incorporates symptom-based diagnosis, mass screening, and both forward and backward contact tracing. By deriving integral equations for the forward and backward tracing rates and coupling them with a Lotka-Euler-type equation for the early growth rate, we obtain a closed deterministic system. This system enables the computation of early growth rates and reproduction numbers under different case-finding scenarios. Using parameter values calibrated from the 2021 Yangzhou outbreak, the theoretical scenario comparisons show that diagnosis alone provides limited control of early epidemic growth, whereas the integrated case-finding scenario substantially suppresses transmission. The results further show that reducing the effective reproduction number below one requires stronger mass screening and contact tracing when infected individuals generate more secondary infections on average. Together, these findings indicate that the theoretical efficacy of case-finding operations depends jointly on intervention intensity and the effective transmission structure.
Xiaoqian Wang, Zhen Jin, Gui-Rong Liu et al.· Journal of Theoretical Biolo...· 0 citations
The accurate estimation of time-varying transmission rates is fundamental for understanding infectious disease dynamics and implementing effective public health interventions. To this end, we propose an improved inverse method for estimating time-varying transmission rates in low-incidence settings, where conventional data pre-processing approaches often fail owing to sparse-case observations. To overcome this difficulty, we introduce an exponential B-spline interpolation approach that integrates both continuous and discrete inverse methods. In addition, we incorporate a non-standard finite-difference method, which enables the reconstruction of epidemic processes under non-equidistant time intervals caused by missing case data. This method ensures that transmission rate estimates remain non-negative and smooth, even when the observed data exhibit low cases or irregularly spaced time points. We apply this approach to several infectious disease models using real-world data from the People's Republic of China and Germany, including a scarlet fever model, a multi-strain influenza model and an age-structured influenza model, as well as a COVID-19 model for Germany. The results show that our method provides accurate transmission rate estimates, particularly in low-incidence infectious diseases, multi-group epidemic models and epidemic datasets with incomplete surveillance records, demonstrating its robustness and applicability across various epidemiological contexts. The improved inverse method offers a new perspective for epidemiological modelling and provides reliable technical support for related theoretical exploration and public health decision-making.
Shuanglin Jing, Yuting Huang, H. Huo· Journal of the Royal Society...· 0 citations
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