In the General Model Theory Stachowiak defined a n-tuple with model. It appears that very consistent with the definition on model as use.
Stachowiak defined <M, O, K, t, Z> as a n-tuple of five parameters (of which) comprising an object O and a model M representing the functional operation F, M= F(O). The object M is a model of object O at time interval t and in reference to the objective Z for a K-system K. 
Understanding by Niemeyer’s paper, the M is model; O is the original of the model, i.e., the object the model modeled; K is the system using the model as a substitute of the O at time interval t with Z; Z is the goal or purpose for K.
It seems very close to the situation in model as use: “where the role carries certain properties of a thing directly or indirectly and works by the properties“. I see this is a certain case of the situation in Model as Use, and I think, is it the case that suitable for all uses of model? The functional operation F, M = F(O), of course, is a mapping. This implies that the model in the Stachowiak’s 5-tuple is one of the types of model in my thoughts, but not all.
 I know a book Allgemeine Modelltheorie (General Model Theory) by Herbert Stachowiak, Wien: Springer, 1973. Unfotunately, so far, I’ve only seen some of fragments by the citations in some literature in English.
 Quotes from: Niemeyer, K. (2007). A Contribution to Model Theory, volume 12 of NATO Science for Peace and Security Series – D: Information and Communication Security. IOS Press.