That’s the sensible thing with a very contagious virus like norovirus (used to be called Norwalk Group Virus). If you get a hundred people through your clinic with noro, the fifty who come in with hangnails will be back in 24 hours with noro.
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It’s the self diagnosis of that ‘it must be the noro virus’ that is dangerous.
I think the NHS requested people to call in rather than visit, so they still talk to a GP or nurse or whatever they have in the UK.
I’ve been to clinics in California where they have special waiting rooms for people suspected of having a contagious disease (influenza in my case). I stood the whole time I waited with my hands in my pockets! I had no idea what the other people waiting in the “special area” had and did NOT want to take it home with me! Norwalk on top of flu would have been an experience to be avoided.