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COVID-19 has brought a significant impact to the global health system, and also opportunities and challenges to epidemiological researches. Theoretical epidemiological models can simulate the process of epidemic in scenarios under different conditions. Therefore, modeling researches can analyze the epidemical trend of COVID-19, predict epidemical risks, and evaluate effects of different control measures and vaccine policies. Theoretical epidemiological modeling researches provide scientific advice for the prevention and control of infectious diseases, and play a crucial role in containing COVID-19 over the past year. In this study, we review the theoretical epidemiological modeling researches on COVID-19 and summarize the role of theoretical epidemiological models in the prevention and control of COVID-19, in order to provide reference for the combination of mathematical modeling and epidemic control.

Objective: In the context of COVID-19 pandemic, the epidemic severities, non-pharmaceutical intervention intensities, individual behavior patterns and vaccination coverage vary with countries in the world. China has experienced a long period without indigenous cases, unfortunately, multi local outbreaks caused by imported cases and other factors have been reported, posing great challenges to COVID-19 prevention and control in China. Thus it is necessary to explore the mechanisms of the re-emerged COVID-19 epidemics and their differences. Methods: Based on susceptible exposed infectious recovered (SEIR) epidemic dynamics model, we developed a set of novel evolution equations which can describe the dynamic processes of integrated influence of interventions, vaccination coverage and individual behavior changes on the re-emergency of COVID-19 epidemic. We developed methods to calculate the optimal intervention intensity and vaccination rate at which the size of susceptible population can be reduced to less than threshold for the re-emergency of COVID-19 epidemic. Results: If strong interventions or super interventions are lifted too early, even a small cause can lead to the re-emergence of COVID-19 epidemic at different degrees. Moreover, the stronger the early control measures lifted are, the more severe the epidemic is. The individual behavior changes for the susceptibility to the epidemic and the enhancement or lifting of prevention and control measures are key factors to influence the incidence the multi outbreaks of COVID-19. The optimist early intervention measures and timely optimization of vaccination can not only prevent the re-emergency of COVID-19 epidemic, but also effectively lower the peak of the first wave of the epidemic and delay its arrival. Conclusion: The study revealed that factors for the re-emergence of COVID-19 epidemics included the intensity and lifting of interventions, the change of individual behavior to the response of the epidemic, external incentives and the transmissibility of COVID-19.