Theoretical foundations and application of the varying coefficient SEIR model

In recent years, various infectious diseases, including coronavirus disease 2019 (COVID-19), have occurred many times around the world, which makes the statistical modeling and analysis of the epidemic particularly important. The modeling and inference of epidemics under government control measures are still worthy of research in this field. In this work, we establish the theoretical foundation for the varying coefficient SEIR model with an attenuation rate, which is built to assess precisely the attenuation stages of the epidemic under control measures. For the model, we discuss the identifiability of the model parameters, analyze the consistency and asymptotic normality of the parameter estimates, and provide the corresponding proofs. Finally, we apply the model to COVID-19 outbreaks in 2020 and simulate daily new cases with the inferred parameters. The simulated case number curve is close to the real data, indicating the usability of the model.