models are run as model tools from toolboxes in arctoolbox or even arccatalog or even within other models. I suspect that one of those requirements isn't being met. If you app doesn't permit access to these, then I suspect it isn't possible to do so in the way you want
Sounds like you have a model that is basically some geoprocessing steps. You could publish your model as a geoprocessing service and then consume the service in you app.
