When a character is first infected, he starts at the Initial effect. Does he keep rolling Endurance until he makes it to either side? Or does he roll once a day or something? The DMG is very unclear on this.
The exact text reference is DMG p49, middle right of the page (in the side bar with the bullet point that says "Disease Progression").
But, to translate...
Basically, the person gets infected and is in the initial stage as you said.
Then,
after he/she takes the next extended rest, roll his endurance check to see if he got better/worse/the same during the night. That endurance check moves him up/down/the same on the disease track.
After each extended rest, roll another endurance check to see how it goes (repeating after each extended rest until the person is either cured or at the final stage)
So, it's kinda/sorta/basically once a day when waking up from an extended rest.
Note: there are other options beyond an endurance check. for instance, instead of an endurance check, you can have an ally tend to you all night and use a Heal check in place of your Endurance check to see how the infected person progresses.. So if the infected person has a low endurance but an ally has a high heal skill, that may be the safer way to go. Or I (think) there is a ritual called cure disease or remove disease or something like that in the PHB1.