Answer:
Allegany County is one of the most rural counties of the state of New York, located in the Upstate part of the state.
Allegany County only has 46,000 inhabitants, and a low population density of 46 people per square mile. The largest town in the county, Wellsvile, only has a bit over 7,000 people.
We can see then, that Allegany County is a predominantly rural place, where people live far apart from each other. In these kind of conditions, it's harder for a disease to spread, hence the low positive case count.
The Bronx is completely the opposite. A fully urban borough, with around 1,400,000 inhabitants, and a population density of 32,903 people per square mile. Besides, the Bronx is characterized by its low-income, socially-vulnerable population, who tend to work jobs where it is easier for the disease to spread (cleaning services, nursing, bus driving, etc).
This is why the Bronx has such a large number of positive cases.
