When we say something is "modeled after" something else, it means that it is based on or follows the same format or style as the original. There are several synonyms for this phrase that can be used interchangeably, depending on the context. Some alternatives are "inspired by," "patterned on," "constructed in the image of," "modeled on," and "emulating." All of these phrases convey the idea that something has been influenced by another, and that there is a strong connection between the original and the copy. In any case, using different synonyms can help vary your writing style and provide a more descriptive and nuanced meaning.