Of course you are always going to interact with N people. Your family consists of n₀ people, there are n₁ people in your office, there are n₂ people around you

Of course you are always going to interact with N people. Your family consists of n₀ people, there are n₁ people in your office, there are n₂ people around you on the train, etc. Area calculations would matter if each infected person somehow densely contaminated an entire circle of a large diameter.