He cautioned South Africans against dropping their guard because "we don't want to squander" this low level.
Karim said: "We were in a similar position in October where we were in very low transmission. In January, however, SA's second wave hit with much higher rates of severe infection than in the first wave, putting health-care workers and hospitals under strain."
Puren said: "The winter months mean closer contact and less ventilation that could certainly contribute to increases in transmission."
The number of people contracting the virus over the next few months would be affected by factors including community immunity, circulating variants and adherence to nonpharmaceutical interventions, such as masks and physical distancing, he said.
University of Cape Town associate professor Sheetal Silal, director of Modelling & Simulation Hub, Africa, repeated the importance of preventative measures.
"Early action by the government and the public is necessary to reduce transmission, which can reduce the size of the peak and may even prevent a new wave," she said.
According to Karim, "no-one knows when and if we are going to have a third wave".
But if it arrives, a third wave would depend on two variables: behaviour and a new variant, he said.
"As we start being more indoors, we are likely to create conditions for the virus to spread. We might start seeing more cases in the latter part of June and July.
"If we get a new variant - and now variants are popping up all the time - it is likely that it will escape immunity, in which case it could lead to a third wave."