overrun

invade in great numbers

• “the roaches infested our kitchen”

occupy in large numbers or live on a host

• “the Kudzu plant infests much of the South and is spreading to the North”

flow or run over (a limit or brim)

seize the position of and defeat

• “the Crusaders overran much of the Holy Land”

run beyond or past

• “The plane overran the runway”

too much production or more than expected

(often followed by `with'' or used in combination) troubled by or encroached upon in large numbers

• “waters infested with sharks”
• “shark-infested waters”
• “the locust-overrun countryside”
• “drug-plagued streets”