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Understanding the processes and mechanisms of the spatial spread of epidemics is essential for making reasonable judgments on the development trends of epidemics and for adopting effective containment measures. Using multi-agent network technology and big data on population migration, this paper constructed a city-based epidemic and mobility model (CEMM) to stimulate the spatiotemporal of COVID-19. Compared with traditional models, this model is characterized by an urban network perspective and emphasizes the important role of intercity population mobility and high-speed transportation networks. The results show that the model could simulate the inter-city spread of COVID-19 at the early stage in China with high precision. Through scenario simulation, the paper quantitatively evaluated the effect of control measures "city lockdown" and "decreasing population mobility" on containing the spatial spread of the COVID-19 epidemic. According to the simulation, the total number of infectious cases in China would have climbed to 138,824 on February 2020, or 4.46 times the real number, if neither of the measures had been implemented. Overall, the containment effect of the lockdown of cities in Hubei was greater than that of decreasing intercity population mobility, and the effect of city lockdowns was more sensitive to timing relative to decreasing population mobility. • A city-based epidemic and mobility model is proposed for simulating the spatial spread of an epidemic between cities. • The effect of "city lockdowns" and "decreasing population mobility" measures were evaluated under ten scenarios. • The effect of decreasing returns to scale and distance decay of population mobility on the epidemic spread were found. [ABSTRACT FROM AUTHOR]