I'm guessing a majority of the deaths would be from the impending global famine. World population would probably take a fucking MASSIVE 'decline', in the billions of people. Like probably less than a billion people on earth in total, as diseases and other horrors run rampant after total societal collapse. I'm also that sure that a lot of governments would continue 'functioning' in some way. Probably governing in a decentralised fashion. Through radio and other ways of communication.