This paper focuses on the dynamics of the COVID-19 pandemic and estimation of associated real-time variables characterizing disease spread. A nonlinear dynamic model is developed which enhances the traditional SEIR epidemic model to include additional variables of hospitalizations, ICU admissions, and deaths. A 6-month data set containing Minnesota data on infections, hospital-ICU admissions and deaths is used to find least-squares solutions to the parameters of the model. The model is found to fit the measured data accurately. Subsequently, a cascaded observer is developed to find real-time values of the infected population, the infection rate, and the basic reproduction number. The observer is found to yield good real-time estimates that match the least-squares parameters obtained from the complete data set. The importance of the work is that it enables real-time estimation of the basic reproduction number which is a key variable for controlling disease spread.