We develop a health informatics toolbox that enables timely analysis and evaluation of the time-course dynamics of a range of infectious disease epidemics. As a case study, we examine the novel coronavirus (COVID-19) epidemic using the publicly available data from the China CDC. This toolbox is built upon a hierarchical epidemiological model in which two observed time series of daily proportions of infected and removed cases are generated from the underlying infection dynamics governed by a Markov Susceptible-Infectious-Removed (SIR) infectious disease process. We extend the SIR model to incorporate various types of time-varying quarantine protocols, including government-level ‘macro’ isolation policies and community-level ‘micro’ social distancing (e.g. self-isolation and self-quarantine) measures. We develop a calibration procedure for under-reported infected cases. This toolbox provides forecasts, in both online and offline forms,as well as simulating the overall dynamics of the epidemic. An R software package is made available for the public, and examples on the use of this software are illustrated. Some possible extensions of our novel epidemiological models are discussed.