As the article suggests only a 'token' of services will operate here is my suggestion:
Durham, Belmont:
6: Every 30 minutes, both buses per hour will operate Durham to Cockfield.
7: Every 30 Minutes.
22: Every 60 Minutes, this service will operate via Easington Collirey.
23: Not Operating, Covered by 22/24.
24: Every 60 Minutes.
43: Every 60 Minutes.
X46: Every 60 Minutes.
48: Every 60 Minutes.
49: Every 60 Minutes.
56/86: Every 60 Minutes.
57: Not Operating.
57A: Every 60 Minutes.
61/62: Normal Service.
64: Every 30 Minutes.
X12: Every 60 Minutes.

Darlington:
1: Every 60 Minutes.
2: Every 30 Minutes.
3: Every 60 Minutes (Town to Skrene Park only).
4: Every 60 Minutes.
5: Every 60 Minutes.
5A: Not Operating.
8: Not Operating.
9/10: Every 30 Minutes.
12: Every 60 Minutes.
13A: Every 20 Minutes (Will Interwork With 3/4.
19: Not Operating.
X21: Every 2 Hours.
X26: Every 60 Minutes.
X66: Every 60 Minutes.
X67: Every 60 Minutes.

Stockton:
5: Every 30 Minutes.
5A: Not Operating.
7A: Every 60 Minutes.
8/9: Every 30 Minutes.
15: Every 20 Minutes.
17: Every 60 Minutes.
17A: Not Operating.
28/29: Combined to operate Every 30 minutes.
X22: Every 2 Hours (Will turn into X21 to Sunderland at Peterlee).

Redcar:
X3: Every 60 Minutes.
X3A: Not Operating.
X4: Every 60 Minutes.
62: Every 60 Minutes.
63: Every 20 Minutes.
64: Every 60 Minutes.
64A: Not Operating.
81: Every 2 Hours.

Whitby: 
X93: Split Route, Service will operate very infrequently.
95: Only Journeys to Grosmont will operate.

THIS IS JUST MY SUGGESTION, I DON'T KNOW WHAT WILL HAPPEN, I DON'T KNOW HOW MANY RESOURCES ARRIVA HAVE, THIS IS JUST MY SUGGESTION TO WHAT COULD POSSIBLY OPERATE.