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In the fight against the COVID-19 pandemic, China has long adhered to the "Dynamic Zero COVID-19" strategy till the end of 2022. To understand the mechanism of this strategy, we used the case of the Yangzhou summer outbreak in 2021 and a multi-stage dynamical model incorporating city-wide and key area testing-trace-isolation (TTI) strategies. We defined two time-varying indexes for measuring the disease transmission risk and the public health prevention and control force, respectively, which allowed us to explore the mechanisms of TTI policies. Integrating with the historical data and literature parameter values, we first estimated the parameters and then quantified the relevant indexes over time. The findings showed that multiple rounds of rapid testing were one of the critical measures to overcome the outbreak in Yangzhou within one month. In addition, we compared the impact of the duration of the free transmission stage, tracking rate, testing interval and precise division of key areas on the epidemiological indicators, including the final sizes of infections and isolations, peak value, peak arrival time and epidemic duration and the minimum round of testing. Our results suggest that the early detection of the epidemic, an improved efficiency of tracking, and a reduced duration of each test play a positive role in restraining COVID-19; however, a considerable investment of resources was essential to achieve a significant effect quickly.

We investigate the dynamics of a differential-algebraic bioeconomic model with two time delays. Regarding time delay as a bifurcation parameter, we show that a sequence of Hopf bifurcations occur at the positive equilibrium as the delay increases. Using the theories of normal form and center manifold, we also give the explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. Numerical tests are provided to verify our theoretical analysis.