Before revision: Traditional methods to infer compartmental epidemic models with time-varying dynamics can only capture continuous changes in the dynamic.However, many changes are discontinuous due to sudden interventions, such as city lockdown and opening of field hospitals .
After revision: Compartmental epidemic models are among the most popular ones in epidemiology. For the parameters (e.g., the transmission rate) characterizing these models, the majority of researchers simplify them as constants, while some others manage to detect their continuous variations. In this paper, we aim at capturing, on the other hand, discontinuous variations, which better describe the impact of many noteworthy events, such as city lockdown and opening of field hospitals .