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We analyze an epidemic model on a network consisting of susceptible-infected-recovered equations at the nodes coupled by diffusion using a graph Laplacian. We introduce an epidemic criterion and examine different isolation strategies: we prove that it is most effective to isolate a node of highest degree. The model is also useful to evaluate deconfinement scenarios and prevent a so-called second wave. The model has few parameters enabling fitting to the data and the essential ingredient of importation of infected; these features are particularly important for the current COVID-19 epidemic., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2020 Elsevier B.V. All rights reserved.)