How about a table with fields of WeekOfYear, Employee, Booked, BookedFor
You would populate the db fields of  WeekOfYear and Employee.  Also
initialize Booked to False And BookedFor  to "".   As you book a week for an
employee change Booked to True and fill in Booked For with the
purpose/Client.
You could then query for weeks available for employee X.

In the alternative you could just record the bookings ( all fields) as they
occur and do some dateMath to figure out what is open.

I would start by reading Albert Kallal's notes on this.  He's done a
LOT of the heavy lifting for you.  If you are _always_ booking full
days, then this is simple.  This works if your rule is:

A person can be assigned at most one job for a single week of the year.

If you have a table
tblBooking(PersonID, WeekNo, Year)

'--apologies for the Oracle syntax, but you get the idea)
CREATE TABLE Booking(
PersonID   INTEGER     NOT NULL,
WeekNo   INTEGER     NOT NULL,
Year         INTEGER     NOT NULL,
PRIMARY KEY (PersonID, WeekNo, Year),
FOREIGN KEY PersonID REFERENCES People(PersonID)

Then the compound primary key creates a unique index (no duplicates) on
the 3 fields.  So you can't insert a duplicate no matter how hard you
try.  So once the date is chosen, you can't choose it again.  You could
also use comboboxes that get their data from select queries that
eliminate unavailable days.  Depends on how your form is set up.