At 0603 GMT, the rand traded at 14.5250 per dollar, 0.12pc firmer than its previous close.
Global financial markets showed some signs of regaining composure after days of heavy selling on fears over the virus.
"Though concerns have not dissipated, there is a renewed sense of calm this morning," RMB said in a morning note.
This comes after the United States confirmed that flights to China are still operational and the outbreak is rumoured to be contained with minimal impact to economic growth, said RMB.
Investors will look for more direction from the U.S. Federal Reserve's policy announcement later in the day.
Government bonds were slightly firmer, with the yield on benchmark 2026, instrument down 2 basis points to 8.065pc.