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Current epidemic models mainly estimate the number of confirmed patients by fitting statistical data. Few studies consider the direct effect of fine-grained spatial crowd mobile interaction on the spatial-temporal diffusion features. A new method for estimating the spatial-temporal spread process of coronavirus disease 2019 (COVID-19) is proposed, incorporating spatial interaction features into epidemiological models. This paper also estimates the number of confirmed patients and spatial-temporal spread process of COVID-19 in Wuhan from December 2019 to March 2020. The results show that the method proposed in this paper can effectively estimate the daily traffic analysis zones (TAZs) where new confirmed patients appear, completely covering the TAZs with the epidemic announcements. And the TAZs with the epidemic announcements account for 72.7% of the estimated TAZs. The cumulative number of estimated confirmed patients agrees very well with the total number of officially announced confirmed patients after February 18, 2020, with a gap of approximately 5.6%, indirectly verifying the rationality of the previous estimation. The method proposed in this paper can effectively estimate the spread of infectious diseases under fine-grained spaces. It also has scientific significance in understanding the influence mechanism of the crowd interaction under finegrained spaces on the spatial-temporal spread of infectious diseases, and enhancing the macroscopically spatial interpretability of epidemiological models macroscopic. [ABSTRACT FROM AUTHOR]