But Sam Querrey, who upset world No 1 Novak Djokovic at Wimbledon, isn't going to Brazil because it just isn't that big a deal to him.
Differing views over the mosquito-carried Zika virus and the rash of recent tennis withdrawals from Rio came out Monday on day one of the ATP and WTA event, the first hardcourt stop on the path to the US Open.
"It's not something you want to take lightly," Stosur said after beating Russian qualifier Alla Kudryavtseva 6-3, 6-0.
"Other people say there are going to be far worse things going on than Zika. It's about being smart, following all the guidelines. I've had all the vaccinations. It certainly has entered my mind this time around."
Several top NBA players, more than 20 men's golfers and several top tennis players have withdrawn from Rio, many but not all citing the potential for contracting Zika, which causes severe illness and has been linked to birth defects.
"I'm kind of scared but I'm not having any kids any time soon so I should be OK," said Stephens, a 23-year-old American set to make her Olympic debut. "Some people are way more sensitive and some people aren't. It just depends on the person."
Canada's seventh-ranked Milos Raonic, who lost the Wimbledon men's final to Britain's Andy Murray earlier in July, eighth-ranked Czech Tomas Berdych and Austria's ninth-rated Dominic Thiem all said no to Rio.
So did 16th-ranked John Isner, the Washington men's top seed, and Querrey, who doesn't see tennis or golf as true Olympic sports.
