If you’re wife is feeling sick you might want to tell them for their help!!
Also, it depends what number child it is, the first child one usually says very early, so parents can rest assured that all is ok… but if it’s a subsequent child you dont have to feel rushed to share the word and can tell them when you feel ready.
No need to tell others (siblings, friends, colleagues…) until you’re showing, unless you just can’t keep a secret!