Encroach (verb)

To gradually take over or intrude on something, especially without permission or right.

Origin:

Late middle english (in the sense "invade, make inroads"): from old french encrochier, from en- "in" + crochir "hook", from croc "hook". the current sense (dating from the mid 17th century) arises from the image of something or someone advancing by hooking or grasping.

Examples:

1. The city's expansion has encroached on the countryside.
2. The neighbor's property is encroaching on my land.
3. The disease is encroaching on his organs.
4. The company is encroaching on the competitor's market.
5. The storm is encroaching on the coast.