Two men, aged 53 and 35, were released, while a 21-year-old woman and 43-year-old man remain in hospital.
So far, 50 suspected cases of the virus had been cleared in NSW.
Dr Chant said people who had been in close contact with the four confirmed cases were being monitored by public health units.
“We’ve got 20 cases currently under investigation and, as I discussed yesterday, that’s a positive sign, that our numbers are increasing, because at the moment we want to increase testing and to make sure we identify every possible case at this current time,” Dr Chant said.
Dr Chant said that the group of 20 consisted of 11 men and nine women, with an age range of five to 74 years.
“As our usual procedure, all of those individuals will be in isolation whilst we’re awaiting test results,” Dr Chant said.
Tests are up and running and at both Randwick and Westmead, which she said will ensure results are provided more quickly.
Thirteen tests on Tuesday night were all negative.