Epidemic model on a network: Analysis and applications to COVID-19

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. •Mathematical analysis of a simple epidemic model on a network.•We introduced an epidemic criterion and examined different isolation strategies.•We evaluated deconfinement scenarios to prevent a second wave.