Robust modeling and inference of disease transmission using error-prone data with application to SARS-CoV-2

Modeling disease transmission is important yet challenging during a pandemic. It is not only critical to study the generative nature of a virus and understand the dynamics of transmission that vary by time and location but also crucial to provide accurate estimates that are robust to the data errors and model assumptions due to limited understanding of the new virus. We bridged the epidemiology of pathogens and statistical techniques to propose a hybrid statistical-epidemiological model so that the model is generative in nature yet utilizes statistics to model the effect of covariates (e.g., time and interventions), stochastic dependence, and uncertainty of data. Our model considers disease case counts as random variables and imposes moment assumptions on the number of secondary cases of existing infected individuals at the time since infection. Under the quasi-score framework, we built an "observation-driven model" to model the serial dependence and estimate the effect of covariates, with the capability of accounting for errors in the data. We proposed an online estimator and an effective iterative algorithm to estimate the instantaneous reproduction number and covariate effects, which provide a close monitoring and dynamic forecasting of disease transmission under different conditions to support policymaking at the community level.