Abstract
We estimate and analyze the time-dependent parameters: transmission rate, symptomatic recovery rate, immunity rate, infection noise intensities, and the effective reproduction number for the United States COVID-19 cases for the period 01/22/2020-02/25/2021 using an innovative generalized method of moments estimation scheme. We assume the disease-dynamic is described by a stochastic susceptible-exposed-infected-recovered-susceptible (SEIRS) epidemic model, where the infected class is divided into the asymptomatic infected, and symptomatic infectious classes. Stochasticity appears in the model due to fluctuations in the disease's transmission and recovery rates. The disease eradication threshold is derived from the reproduction number. The estimated parameters are used to model the disease outbreak's possible trajectories. Our analysis reveals that current interventions are having positive effects on the transmission and recovery rates. The analysis is demonstrated using the daily United States COVID-19 infection and recovered cases for the period: 01/22/2020-02/25/2021.