By considering the recently introduced SIRU model, in this paper we study the dynamic of COVID-19 pandemic under the temporally varying public intervention in the Chilean context. More precisely, we propose a method to forecast cumulative daily reported cases $CR(t)$, and a systematic way to identify the unreported daily cases given $CR(t)$ data. We firstly base on the recently introduced epidemic model SIRU (Susceptible, asymptomatic Infected, Reported infected, Unreported infected), and focus on the transmission rate parameter $\tau$. To understand the dynamic of the data, we extend the scalar $\tau$ to an unknown function $\tau(t)$ in the SIRU system, which is then inferred directly from the historical $CR(t)$ data, based on nonparametric estimation. The estimation of $\tau(t)$ leads to the estimation of other unobserved functions in the system, including the daily unreported cases. Furthermore, the estimation of $\tau(t)$ allows us to build links between the pandemic evolution and the public intervention, which is modeled by logistic regression. We then employ polynomial approximation to construct a predicted curve which evolves with the latest trend of $CR(t)$. In addition, we regularize the evolution of the forecast in such a way that it corresponds to the future intervention plan based on the previously obtained link knowledge. We test the proposed predictor on different time windows. The promising results show the effectiveness of the proposed methods.