In this paper, a new compartmental mathematical called Susceptible-Exposed-Symptomatic Infectious-Asymptomatic Infectious-Quarantined-Hospitalized-Recovered-Dead (SEIDIUQHRD) has been proposed and calibrated for interpreting the transmission dynamics of the novel coronavirus disease (COVID-19). The purpose of this study is to give a tentative predictions of the epidemic peak time and size for different COVID-19 hotspots in the world by using a newly developed optimization algorithm based on well-known trust- region-reflective (TRR) algorithm, which is one of the robust real-time data fitting techniques. Model parameters can be calibrated successfully by using this algorithm. In addition, the basic reproductive number (R0) which is the most insightful metric in understanding the outbreak dynamics, has also been calculated for different countries. It has been enlightened in our analysis that the pandemic is not going to fade out early. Moreover, Latin hypercube sampling-partial rank correlation coefficient (LHS-PRCC) which is a global sensitivity analysis (GSA) method has been applied to quantify the uncertainty of our model mechanisms. From this analysis, the most dominating model mechanisms can be traced out. Our analysis suggest that direct transmission rate, efficacy of quarantine and physical distancing restrictions could be the most sensitive parameters in controlling the outbreak. The public health implication of this is that, we cannot afford lifting up social distancing restrictions and public health guidelines too early. Keywords: Compartmental model; COVID-19; asymptomatic carrier; quarantined class; model calibration; forecasting; sensitivity analysis.