Objectives: Diseases such as SARS-CoV-2 have novel features that require modifications to the standard network-based stochastic SEIR model. In particular, we introduce modifications to this model to account for the potential changes in behavior patterns of individuals upon becoming symptomatic, as well as the tendency of a substantial proportion of those infected to remain asymptomatic. Methods: Using a generic network model where every potential contact exists with the same common probability, we conduct a simulation study in which we vary four key model parameters (transmission rate, probability of remaining asymptomatic, and the mean lengths of time spent in the exposed and infectious disease states) and examine the resulting impacts on various metrics of epidemic severity, including the effective reproduction number. We then consider the effects of a more complex network model. Results: We find that the mean length of time spent in the infectious state and the transmission rate are the most important model parameters, while the mean length of time spent in the exposed state and the probability of remaining asymptomatic are less important. We also find that the network structure has a significant impact on the dynamics of the disease spread. Conclusions: In this article, we present a modification to the network-based stochastic SEIR epidemic model which allows for modifications to the underlying contact network to account for the effects of quarantine. We also discuss the changes needed to the model to incorporate situations where some proportion of the individuals who are infected remain asymptomatic throughout the course of the disease.

A common method of checking person‐fit in Bayesian item response theory (IRT) is the posterior‐predictive (PP) method. In recent years, more powerful approaches have been proposed that are based on resampling methods using the popular Lz∗$L_{z}^{*}$ statistic. There has also been proposed a new Bayesian model checking method based on pivotal discrepancy measures (PDMs). A PDM T is a discrepancy measure that is a pivotal quantity with a known reference distribution. A posterior sample of T can be generated using standard Markov chain Monte Carlo output, and a p‐value is obtained from probability bounds computed on order statistics of the sample. In this paper, we propose a general procedure to apply this PDM method to person‐fit checking in IRT models. We illustrate this using the Lz$L_{z}$ and Lz∗$L_{z}^{*}$ measures. Simulation studies are done comparing these with the PP method and one of the more recent resampling methods. The results show that the PDM method is more powerful than the PP method. Under certain conditions, it is more powerful than the resampling method, while in others, it is less. The PDM method is also applied to a real data set.