COVID-19 transmission methods mainly include direct transmission, aerosol transmission and contact transmission. When COVID-19 was prevalent in the early stage, China adopted tracing isolation measures. Due to the complexity of the network topology, we can use the dimensionality reduction method to convert the mean-field model in the general network into an equivalent, simpler low-dimensional model. We can discuss the stability of the disease-free equilibrium and the endemic equilibrium, and then calculate the basic reproduction number and the precise expression of the final size. Based on this, a dynamic network is established to study the transmission dynamics model of COVID-19 in the case of tracing isolation. Besides, the differential equations of degree distribution, the first moment and the second moment of dynamic network with respect to time t and the number of populations in society in each state can be deduced at different initial time of implementing the tracing isolation policy. Our research results can provide some guidance for the prevention and control of the contact transmission of COVID-19, and provide new ideas for the control of network infectious diseases.