Compulsory vaccination against Covid-19 isn't going to happen in most countries. Or is it? It can be made a condition of employment, travel or entry.
There are precedents for this. If you want a job as a doctor, you have to have the right qualifications and certificates. If you want to go to university, you have to have achieved a level of academic achievement. If you want a job as a typist, you have to be able to type. If you want to come to the UK from Pakistan, you have to have been vaccinated against polio.
So what jobs might require a current certificate of vaccination? Suppose there were two airlines; one is able to advertise that all cabin staff are vaccinated, the other isn't. Which would you prefer to travel on? Same with supermarkets, shops, pubs. If a pub can have a policy of "no shirt, no shoes, no entry" then it can also have a policy of "no vaccination, no entry".
Once Covid vaccinations are generally available, I would expect that at least some employers will make it a condition of employment, that you have current vaccinations. I would expect that pretty much all international travel will require a vaxcert. That when cruises restart, they will require vaxcerts. That taxi drivers will display a vaxcert, and people will prefer those. And so on, and so on.
So vaccination might not be compulsory, but getting vaccinated will confer so many advantages that many people will prefer to be vaccinated.