Model structure arising from one hereditary cotorsion pair on extriangulated categories

Let C be a weakly idempotent complete extriangulated category. In contrast with the Hovey correspondence of admissible model structures on weakly idempotent complete exact categories from two complete cotorsion pairs, we give a construction of model structures on C from only one complete cotorsion pair. Our main result not only generalizes the work by Beligiannis-Reiten and Cui-Lu-Zhang, but also provides methods to construct model structures from silting objects of C and co-t-structures in triangulated categories.