I've been mulling over a way to create a post-apocalyptic world where all plant life in densely populated areas have died off and caused humans to die from lack of oxygen. In this world I would like a few small islands that still support human life, I dont want to have to put it in a dome to keep the oxygen from being sucked into the atmosphere if possible. Im thinking a very dense jungle. I'm also wondering what the smallest size I can make this these islands for this idea to be plausible
You Cannot Survive on an "Oxygen Island"
Consider standing on an island, somewhere near the beach. While the sun is a bit hot there is a wonderful breeze coming off the ocean to cool you. Except this is your world where oxygen does not exist outside of the island except in trace quantities. You breathe in, but your lungs are only sucking carbon dioxide and nitrogen. Within two breaths you become very tired, and with another you fall to the ground. And that's how you die... seemingly relaxing near the beach.
That's the problem with a lack of available Oxygen. Having no available Oxygen is not synonymous with not having any atmosphere; you still have wind, and that wind is going to be lethal. With a single good gust of wind (as occurs regularly on islands, and everywhere) your entire population dies almost instantly. The problem would actually be made much worse by a lack of plants in other areas, as wind speeds would increase globally - driving more deadly wind your way.
Also, your jungle won't create an "oxygen bubble" that people can live in; trees are not THAT efficient at scrubbing oxygen for us, and are even worse at trapping it into habitable zones. Trees aren't even the major contributor of oxygen to the world; look to grasses and algae for that.
You do not need to run out of oxygen in order to make people and plants die. Just dial up the atmospheric pressure and your good friend oxygen toxicity rears its ugly head.
You see, when you breathe too much oxygen, you die! Or more specifically, when atmospheric pressure is higher than 8 atmospheres, you are getting too much oxygen every time you take a breath. The resultant symptoms are nasty, and depending on the length of exposure, fatal. Your people won't drop dead as soon as they venture into a zone like this, but they will not be able to live there for prolonged periods of time.
High amounts of oxygen also increase oxidative stress on plants. This will interfere with their natural cycles and also kill them.
However, those living at very high elevations will experience lower atmospheric pressure, and thus avoid the effects of oxygen toxicity and oxidative stress. Your "islands" become tall mountain peaks, in an "ocean" of deadly oxygen.
If whatever event that causes this change, was either caused or could cause in increase in sea levels and/or a drastic change in temperature then a mini atmosphere around the island(s) would form because all other land would be too cold, or too hot to exhibit life, or simply underwater. There would need to be more oxygen produced that used because a lot of it would dissipate to the rest of the globe, however if the air around the island(s) was warmer than the rest of the atmosphere due to the energy releasing activity on the island(s) then the particles of air would be more likely to stay inside the mini atmosphere because they move faster that the other air particles. For this idea to work you would need to reason for all the humans everywhere else to die to be something different than lack of oxygen, more likely lack of food supply (due to the increase in water levels) or too hot/cold temperatures for life.