Change in Climate

I am doing a research project on Supervolcanoes and their climate effects. If I were to (hypethetically) say that The supervolcano under Yellowstone National Park were to erupt, I know that the surfuric acid cloud would kill everything within between 250-700miles, create a nuclear winter, result in lower temperatures by 10-15C, and destroy our ecosystems.

How long would it take before the ecosystems were able to recovery, and how long would (the remainder) of humans be forced to survive with limited vegetation? And how long would the nuclear winter last? (I have heard people state between 4-5years, up to 10-12 years?)

Thanks for any possible assistance.