There has been some confusion regarding immunity to reinfection with COVID-19 in the 3 months after infection. The study shows that people can continue to test positive for 3 months after diagnosis and not be infectious to other people. This does not imply that a person is immune to reinfection in the 3 months following infection. The data simply suggests that retesting someone in the 3 months after initial infection is not necessary unless that person is exhibiting symptoms of COVID-19 and those symptoms cannot be associated with another illness.

The CDC suggests that people with COVID-19 should be isolated for 10 days after symptom onset and until 24 hours after their fever subsides without the use of fever reducing medications.

More than 15 studies have shown that the amount of live virus found in the nose and throat drop significantly soon after symptoms develop. Additionally, the infectiousness of most people is no longer than 10 days after symptoms begin and no longer than 20 days in people with severe illness or those who are severely immunocompromised.

https://www.cdc.gov/media/releases/2020/s0814-updated-isolation-guidance.html