Let’s not pretend that desert expansion is a result of human activity.
I gather you are not familiar with the Younger Fill and the argument Emmett Scott gave for its origin in his book Mohammed and Charlemagne Revisited.
There is a layer of silt in the Mediterranean that dates to the rise of Islam, and, Scott argues, provides archaeological evidence for Pirenne's thesis that the rise of Islam was the cause of the Western European Dark Ages. A great deal of modern desert in North Africa and Palestine had been the breadbasket of the Roman Empire, and its desertification was cause by overgrazing after the Muslim conquest -- Muslims taking the attitude that land, including agricultural land, owned by non-Muslims was grazing range for the herd animals of Muslims. Wind erosion of the overgrazed former farms created the Younger Fill, and left behind the modern deserts of Palestine and coastal Libya.
Desert expansion is, sometimes the result of human activity, in the form of overgrazing in already arid, but not quite desert, conditions.