What mathematical models are recommended for estimating non-organic download uplift at launch?

I think it'd be hard to come up with a "model" for this a priori, unless you use past app launches as comparables. 

I gave a GDC talk about how my team tried to estimate organic contributions for a game launch way back in 2014; a lot of the specific data there is dated but I think the overall approach is still valid. What I generally do in launch situations is to scenario plan for a variety of different outcomes with respect to organic outcomes, eg. here is a sensitivity matrix that gives us guidance on what we can bid / how much budget we can deploy given various levels of organic contribution. 

If the model you're referring to relates to bid prices given different levels of organic installs, then that wouldn't be any different in launch than in a "live" setting, although you'd have less information about the value of organic users.