Objectives: In this paper, we aim to propose the efficient and interpretable models to study and predict the evolution of COVID-19 pandemic, which is in particular not limited to the setting the epidemic ends with one wave, and the public intervention is varying. In this setting, we firstly propose a novel method to infer the transmission rate on the top of the recently introduced SIRU model. Next, we establish the link between the transmission rate and the public intervention. Lastly, we propose a forecasting model for the cumulative daily reported cases, CR(t). Methods: Firstly, we incorporate the nonparametric estimation into SIRU system to obtain a precise reconstruction of the transmission rate dynamic. We then rely on the logistic regression to set up a prediction model for this dynamic given the variable public intervention. Lastly, we propose a regularized the polynomial approximation which considers the SIRU structure and the future public intervention to predict the cumulative daily reported cases. Results: We demonstrated the proposed methods with the Chilean data. The inferred transmission rate exhibits the consistent thus interpretable dynamic with respect to the variable public intervention. To evaluate the performance of the CR(t) predictor, we considered two time points after 9 months since the first breakout of the epidemic, and obtain the one-month prediction starting from these time points. The proposed predictor is able to give the accurate prediction, sometimes even with imperfect regularization hyperparameter. Conclusions: This work provides a methodology to combine the machine learning methods with the compartmental models, to enhance the later with data. Firstly, the novel inference method for the transmission rate has made the SIRU model applicable to the setting with multiple waves and the varying public intervention. Moreover, the proposed technique is transferable to other compartmental models. Secondly, the proposed predictor of CR(t) can consider the varying public intervention, and thus is able to provide valid prediction for one month long, which is a great advantage compared with its competitor in literature.