I get messages that my phone is infected by viruses

Ignore it: it's a scam. No-one can remotely detect that you have a virus (which you don't anyway). Without exception, all messages telling you you have a virus, that you are being hacked, or that your ID is about to be closed, are scams. they are trying to get you to reveal your ID and password, or to sell you uneccesary and expensive software.

Never follow links, ring numbers, or follow instructions in unexpected emails.

'Calendar spam' is all too common. I would suggest you repost your question in the iCal forum, https://discussions.apple.com/community/applications/ical, where someone may be able to advise.

my calendar fills every hour with alerts about my phone being infected

do you know what to do with that?