given the cayos happening in the world i wouldn't be surprised of nuclear war and in this case i would expect internet disruption question is how do we trade bitcoin during this time if we can't access internet.
home internet and mobile internet goes down
You don't. Seriously this is the stupidest question I have ever heard. In the event of a nuclear war - your primary concern is bitcoin trading. It's actually a pretty good argument to have a nuclear war - sort of weed out the genetic evolutionary reversal that seems to be occurring in a vast proportion of the human species.
What is more likely in the near term is large, rolling regional, national blackouts/power outages etc due to hackers. If you are in a situation like that, you will want to have some sort of physical monetary or bartering system. But in those situations, the power will eventually come back on, and while there might have been chaotic disruption/looting/ etc.... the Internet will again power up, and your bitcoins will still be out there.
But if you are in Pakistan/India or N Korea/S Korea or Israel/Iran - the sites of the most probable, initial "limited" nuclear tradeoff zones - then yes, your bitcoin trading will most likely be disrupted for a bit. But it will be helpful after you have migrated cross border into a new land, one where the power still works, bitcoin was never impacted etc. And you'll have your bitcoin capitol to rebuild your life.
Of course, once the final war with the AI / ZombieBorgs starts, THEN you'll want the gold/silver and bitcoin/internet will be under enemy control, and then ultimately gone.