abstract: Our objective in this study is to develop a model that can directly use the observed data (tests, cases, or deaths) to recover the time-varying efficacy of local non pharmaceutical interventions by dynamically identified delays. There are several recent examples in the literature that also use positivity rates and case numbers based on multinational panel datasets, where the delays in the effect of mobility changes, however, are not estimated dynamically but assumed to be constant during the entire period of analysis. We have developed and trained a non parametric algorithm inspired by Gaussian Graphical Models that have been recently and extensively used in genomics, finance, neuro imaging, and other fields that require network analysis on high-dimensional data. In our initial application, we have tested our method and compared Montreal, Toronto, and New York. We find that the mobility restrictions are least capable of fighting the spread in Montreal than in Toronto and New York, although the average mean-maximum correlations are similar in these cities. Our counterfactual simulations reveal that the low efficacy of mobility restrictions in Montreal might be related to a lower public sensitivity toCOVID-19 and that the average reduction in mobility relative to the spread might not have been enough in terms of its magnitude and speed compared to other cities