I define eradicating disease on a global scale to be a "tough task".
That's relevant enough for me.
Canada's G-20 suggestion deserves looking into, and possibly supporting. (Who would be the reps from Africa? Would Chile consider Brazil, Argentina and Venezuela to be acceptable reps? Doubtful...) An organization designed by post-WWII leaders is bound to be out of step with the post-Cold War world. Political institutions need to evolve, too. It's actually kind-of exciting.
I note, however, that your two specifically named betes noires, Russia and China, would be included in G-20, as well they must, since nothing can be accomplished on a global scale without such a sizable portion of the Earth's landmass and population. The more things change, the more they remain the same, eh?