Sunday as a Week Marker

Solution 1:

My own convention and that which is standard in the UK is to say either 'Week commencing 10th February', or 'week ending 16th February', where 10th is Sunday and 16th is Saturday. These are abbreviated as follows;

w/c 10/2/14 w/e 16/2/14

Both refer to the same week.

Solution 2:

According to Wikipedia,

For most observant Christians, Sunday is observed as a day of worship and rest, holding it as the Lord's Day and the day of Christ's resurrection.

In some China countries and Israel, Sunday is the first work day of the week.

According to the Hebrew calendar and traditional Christian calendars, Sunday is the first day of the week.

But according to the International Organization for Standardization ISO 8601, Sunday is the seventh day of the week.

This means that there isn't universal agreement about whether Sunday is the first or last day of a week. Different people adopt different stances.

This means that people will not agree about whether a Sunday 'belongs' in the 7 day period finishing on that Sunday or starting on that Sunday. (Some might even want a Wednesday-Tuesday 'week', cf the financial year.)

The phrase 'the week of the 24th' (being a Sunday) is, as OP suggests in a comment, correspondingly ambiguous. Though it is likely that few would use just an end date to define a week.