Going into conspiracy theory mode.....
People who get vaccinated will be given a Vaccination Certificate, maybe in the form of a credit card sized plastic card with your photo and other personal details printed on it and embedded in a readable chip. To do pretty much anything you will have to either show the card to someone ie at a job interview or airport check in desk, or scan the chip on a reader at say a supermarket or cinema entrance. It will be mandatory to carry the card at all times and the Police will have powers to stop people and demand they produce the card.
The other possibility is that the vaccine will contain a nano chip that will lodge under the skin and we will all be chipped like dogs!
I love a good conspiracy theory!