Fig. 1

Illustration of the model process considering the implementation of CTTI in the Zero-COVID policy. a The schematic diagram of the model. The flow chart of the model in b free transmission stage c contained transmission stage. All individuals are in different states, Susceptible (S), Exposed (E), Infected (asymptomatic A, presymptomatic \({I}_{1}\) or with symptoms \({I}_{2}\)), Recovered (R) or Deceased (D). If the confirmed cases were detected, we also include the diagnosed and isolated (\({I}_{d}\)) and the individuals admitted to ICU (\(H\)). The traced and isolated susceptible, exposed, asymptomatic and presymptomatic infected populations are described as \({Q}_{S}\), \({Q}_{E}\), \({Q}_{I}\), respectively. In the contained transmission stage, the arrow with orange color represents the process of contact tracing, while the green arrow shows the process of citywide testing and symptomatic testing. All the confirmed and traced individuals are isolated in the designated isolated facilities. The description of parameters shown in the flow diagram can be found in Table 1. \({T}_{0}\): initial time, \({T}_{1}:\) the date when the first infection is confirmed, \(T\): the time needed to complete one round of citywide testing, \({T}_{2}\): the time when no new infections are detected. CTTI: citywide test-trace-isolate