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We give some equivalent characterizations of $\mathcal{GP}$, the class ofGorenstein $(\mathcal{L}, \mathcal{A})$-projective modules, and construct somemodel structures associated to duality pairs and Frobenius pairs. Moreover,some rings are described by Frobenius pairs. Meanwhile, we investigate stronglyGorenstein $(\mathcal{L}, \mathcal{A})$-projective modules and obtain someequivalent characterizations of them. Also, some model structures andrecollements associated to strongly Gorenstein $(\mathcal{L},\mathcal{A})$-projective modules are constructed.

Model structures and recollements induced by duality pairs