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We develop a new Bayesian construction of the elastic net (ENet), with variational Bayesian analysis. This modeling framework is motivated by analysis of gene expression data for viruses, with a focus on H3N2 and H1N1 influenza, as well as Rhino virus and RSV (respiratory syncytial virus). Our objective is to understand the biological pathways responsible for the host response to such viruses, with the ultimate objective of developing a clinical test to distinguish subjects infected by such viruses from subjects with other symptom causes (e.g., bacteria). In addition to analyzing these new datasets, we provide a detailed analysis of the Bayesian ENet and compare it to related models.