How does oxygen reach and circulate in regions that have no or very little plants like Africa or the middle of the ocean?

The atmosphere is a very well-mixed fluid, basically, and oxygen production is relatively constant over time, so there is no delay factor to worry about.  the distribution paths are always pretty much filled.  The air moves around a lot, and fairly quickly. the down side to this well-mixed system is that pretty well everywhere on earth is contaminated by our pollutant discharges.

The air moves around the earth at rates of a few weeks to totally circle the earth at a particular latitude, to rates of several months across a hemisphere in the N-S direction, to perhaps a few years when crossing from one polar region to another (the equatorial region is somewhat of a mixing barrier, or really a zone of slower mixing, that somewhat separates northern hemisphere from southern hemisphere).

It is basically a steady state system, because oxygen is always being produced and being moved.  If production were highly seasonal and localized as to place of origin, then we might actually see cyclical or spatial variations in O2 in air as a result, but we do not really see that.   There is some, but it is not a major variation.

It is not really primarily a "dissipation" process (it is convection-dominated, not diffusion-dominated).  that is, it is active flow and mixing rather than slow spread from a source of high concentration to zones of low concentration.

Air currents move air around the entire planet, regardless if there are plants or not.

The earth's atmosphere has 20% oxygen. All gas molecules move from where they are abundant to where they are less abundant. It is called diffusion. 

Think of the atmosphere as a gigantic machine that moves stuff around the planet.  Marine plants, plankton, land plants produce oxygen which goes into the atmosphere.  The warm air rises and the rotation of the earth moves the air all around the planet. This movement of the air is what we call weather.  

SOME parts of Africa have few plants, but much of Africa is well provided with vegetation of all sorts. The huge basin of the River Congo (much bigger than the Mississippi/Missouri basin) is mainly jungle or rain forest, as are other areas of Africa.

Well first of all, the ocean produces 50~80% of the world's oxygen. Ocean plants, plankton and algae that can photosynthesize does this.

As for barren dessert regions, the Earth's atmosphere is created in large part by the planet's gravitational force that prevents its gasses from dissipating into space. Oxygen produced in other parts of the planet is then dissipated internally within that atmospheric space, so that air of barren dessert would be filled with oxygen produced elsewhere. In chemistry, this phenomenon is known as "diffusion". I won't define it for you, you can Google it and it's fairly easy to understand.