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Coronaviruses, including SARS-CoV, MERS-CoV, and SARS-CoV-2 cause respiratory diseases with remarkably heterogeneous progression. This in part reflects the viral ability to influence the cytokine secretion and thereby the innate immune system. Especially the viral interference of IFN-I signaling and the subsequent deficiency of innate immune response in the early phase have been associated with rapid virus replication and later excessive immune responses. We propose a mathematical framework to analyze IFN-I signaling and its impact on the interaction motif between virus, NK cells and macrophages. The model recapture divergent dynamics of coronavirus infections including the possibility for elevated secretion of IL-6 and IFN-γas a consequence of exacerbated macrophage activation. Dysfunction of NK cells recruitment increase disease severity by leading to a higher viral load peak, the possibility for excessive macrophage activation, and an elevated risk of the cytokine storm. Thus the model predicts that delayed IFN-I signaling could lead to pathogenicity in the latter stage of an infection. Reversely, in case of strong NK recruitment from infected cells we predict a possible chronic disease state with moderate and potentially oscillating virus/cytokine levels.