The Corona Virus Disease 2019 (COVID-19) emerged in Wuhan, China in December 2019. In order to control the epidemic, the Chinese government adopted several public health measures. To study the influence of these measures on the transmissibility of COVID-19 in the city of Wuhan and other cities in the Hubei province, China, we establish generalized semi-varying coefficient models for the number of new diagnosed cases and estimate the varying coefficient for the covariates by the spline method. Since the pandemic was most severe in Wuhan, we fitted separate models for Wuhan and the remaining 16 cities in Hubei. Estimators for the incubation periods, the real-time transmission rates, and the real-time reproduction numbers were obtained. The results demonstrate that the changes in the real-time transmission rate in Wuhan and other cities in Hubei are almost simultaneous. Futher, public health interventions such as restriction of traffic, adjustment of the diagnosed standard, deployment of medical resources, and improvement of nucleic acid testing capacity, had positive effects on reducing the transmission of COVID-19.