The condition is linked to birth defects amongst babies and has been spreading across the Americas – including Brazil where the games will be held.
The Sunday Times is reporting the team's medical adviser says the risk of catching it may increase after athletes finish competing as they'll be more relaxed and may let their guard down on preventative measures.
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Anyone travelling to region is also being warned not to have unprotected sex for at least six months after returning – as the virus may be sexually transmitted.