Define a non-Desert for food
Can you provide minimum examples of when a person in transit has left the desert and is now in close proximity to a sufficient source. e.g. Does a weekend Farmers Market qualify? Are we only to consider major Super Markets?
Kenneth Blacks commented
Farmers Markets can be included with your analysis, as well as any other forms of food/grocery (ie. butcher, cultural food shops, etc). Perhaps you can use buffers to assist with your solution(s). How far would the average person walk to get basic services and needs? How can people with limited mobility access food if they live in a low income area, within near a food desert? What type of transfers may need to be considered? Or, is there room to improve, modify or expand Mobility on Demand? Consider the round trip from point of origin (ie. front door, work) - to transportation option – to point of destination (ie. store) – and back.