Help with using Triggers MySql/Innodb

MySql Gurus

This may be the wrong mailing list for this question, so I apologize 
in advance for breaking some rule.

I'm trying to get a trigger to work.  My environment is a Perl DBI 
interface to a MySql database on Centos 6.  I use the InnoDB database.

I have two tables involved in this operation:

table:  House, with fields:
   HouseID INT AUTO_INCREMENT
   PeopleCount INT
   <other fields not relevant to this discussion>



Table:  People, with fields
   PeopleID INT AUTO_INCREMENT
   HouseID INT  (shows which house the person belongs to)
   Name VARCHAR(30)
   <other fields not relevant to this discussion

Whenever I insert (or delete) a row to the People table, I want the 
PeopleCount in the House (identified by the HouseID in the people 
table) to be incremented or decremented.

My latest attempt is a trigger:

CREATE TRIGGER after_insert_people AFTER INSERT ON People FOR EACH ROW
  BEGIN
   UPDATE House SET PeopleCount = PeopleCount + 1 WHERE HouseID = 
People.HouseID;
  END


The trigger gets "triggered", but a diagnostic says that 
"People.HouseID" is an undefined column.

Any clues would help.

Thanks
David