Swagger: Spring MVC models in GET request

In MVC, you would expect that controller will receive models as input and produce models as output. In Swagger, the latter is not a problem but I have troubles with former. I can't understand how to make Swagger build an input model from incoming GET parameters.

Consider:

"paths": {
    "/search": {
        "get": {
            "consumes": [],
            "produces": [
                "application/json"
            ],
            "parameters": [
                // What goes here?
            ],
            "responses": {
                "200": {
                    "description": "Success",
                    "schema": { 
                        "$ref": "#/definitions/SearchResponse"
                    }
                },
            }
        }
    }
}

How do I make the generated controller's method to have a signature like:

    public ResponseEntity<ResultModel> controllerGet(ModelFromParameters input);

where ModelFromParameters will have several fields corresponding to different GET parameters.

Examples mostly focus either on POST requests, or GET requests where every of 20-odd parameters are stuffed in the arguments list of method, which is obviously anti-MVC.

The API in question is a complex stateless querying system with a lot of parameters.