https://thehill.com/changing-america/well-being/prevention-c...
You can debate whether or not it's really a reinfection or not, but no one is going to really know for sure until quite some time and further studies can be done.
So for now, I wouldn't count on immunity after catching the disease.
I'd personally watch any publication from Singapore in this regard - one of their primary learnings from SARS was to become a biotech hub which enabled them to rapidly scale testing in this case and you can assume they have very good surveillance of existing cases.
https://www.moh.gov.sg/covid-19
They share details on all cases, along with the result of the investigation around whom they have been in contact with and where they have been.
They also created a dashboard with all information: https://experience.arcgis.com/experience/7e30edc490a5441a874...
"THREAD/1: We saw now several reports of reinfection and I wanted to talk a little about that. While immunity induced by SARS-CoV-1, MERS-CoV and human CoVs is not very long lived, an immune response is typically induced and antibodies persist for 1-3 years."
"2) Now, there is evidence that people with COVID19 mount an immune response (e.g. https://medrxiv.org/content/10.1101/2020.02.20.20025841v1). That makes re-infection, especially short-term extremely unlikely. What is more likely is, that the patient is still shedding virus but some of the tests were negative."
"3) Follow up tests can turn positive after a few negative tests, e.g. because sampling was better. Also, and this is a very important point, just because somebody still tests positive in a nucleic acid based test, does not mean they are still shedding infectious virus."
"4) E.g. Measles RNA can be detected for months in patients, long after infectious virus shedding has stopped. This is also the case for other viruses. And I think this is the most likely scenario here."
https://twitter.com/florian_krammer/status/12333387467890360...