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There must be sufficient resources for the cats to survive. Either someone is feeding them or there is an ample supply of mice, rats or whatever. You can trap and remove all you want but unless you get rid of the food source, they (cats) will re-populate the area. Experts say the only solution is TNR (trap, neuter and release). Many don't understand the release part but that is the secret to controlling the population. An area will only support so many cats. Normally, this is such a small number of cats per square mile that one hardly notices (or sees) them. Like someone has already stated, I'm betting you have a hoarder or at the very least, someone who is providing plenty of food.