Reports suggest less than 50% of professional tennis players have been vaccinated.
Williams has not played a single match since Wimbledon this year.
Barty will next appear on Sunday for the final match of the tournament.
Nadal has been forced to put a stop to the rest of the 2021 season.
Murray eventually beat Basilashvili in four sets.
Stephens defeated Karolina Muchova in straight sets.
Williams defeated Mihaela Buzarnescu in the second round.
Osaka was fined $15,000 for not partaking in compulsory media appearances.
Osaka has cited mental health as the reason behind her decision.
Williams lost the match 7-6 (4), 6-2.