The police generally have a right to go to all public areas to enforce an arrest warrant. Again, generally, they also need a search warrant (obtained with probable cause) to enter the residence of a third party to effect an arrest. That can change if the owner gives permission for the police to enter or, in some states/circuits, the police actually see the targeted person and the person retreats deeper into the house. (4th amendment gives a reasonable expectation of privacy. In some circuits, like the 9th, if one were to expose the wanted person when he opened the door, that might be enough for the police to do an entry under exigent circumstances.) I'm not going to look up Mississippi as the facts get so closely read in these cases to require multiple cases to really show what the police can do if the owner actually exposes the person targeted by the warrant.
If the police actually do believe the targeted person is in the house, they can keep everyone from entering and exiting until they do get a search warrant--where they can then enter.