We present a phylodynamic and phylogeographic analysis of this new severe acute respiratory syndrome coronavirus 2 (SARS‐CoV‐2) virus in this report. A tree of maximum credibility was constructed using the 72 entire genome sequences of this virus, from the three countries (China, Italy, and Spain) available as of 26 March 2020 on the GISAID reference frame. To schematize the current SARS‐CoV‐2 migration scenario between and within the three countries chosen, using the multitype bearth‐death model implemented in BEAST2. Bayesian phylogeographic reconstruction shows that SARS‐CoV‐2 has a rate of evolution of 2.11 × 10 −3 per sites per year (95% highest posterior density: 1.56 × 10 −3 to 3.89 × 10 −3 ), and a geographic origin in Shanghai, where time until the most recent common ancestor (tMRCA) emerged, according to the analysis of the molecular clock, around 13 November 2019. While for Italy and Spain, there are two tMRCA for each country, which agree with the assumption of several introductions for these countries. That explains also this very short period of subepidermal circulation before the recent events. A total of 8 (median) migration events occurred during this short period, the largest proportion of which (6 events [75%]) occurred from Shanghai (China) to Spain and from Italy to Spain. Such events are marked by speeds of migration that are comparatively lower as compared with that from Shanghai to Italy. Shanghai's R 0 and Italy's are closer to each other, though Spain's is slightly higher. All these results allow us to conclude the need for an automatic system of mixed, molecular and classical epidemiological surveillance, which could play a role in this global surveillance of public health and decision‐making.