After people have COVID-19, they probably become immune. Many convalescent patients developed SARS-CoV-2 neutralizing antibodies, IgM, and IgG, which decreased months later (Klar; Lei et al.; Long et al.; Seow et al.; Wajnberg et al.). Memory T cells, CD4+ helper T cells, CD8+ killer T cells, and memory B cells, which are kinds of white cell lymphocytes, develop and provide longer-lasting immunity (Calhoun et al.; Grifoni et al.; Mandavilli “Can you get COVID-19 again?”; Ni et al.; Resnick, Irfan; Robbiani et al.; Sekine et al.; Thieme et al.). Consequently, patients with no detectable antibodies might still be immune (Gorvett; Resnick, Irfan).
Some had COVID-19 symptoms for months, most testing positive for viral RNA, and some not (Garner; Mandavilli; Yong “COVID-19 can last..”). Some apparently recovered, had no symptoms or viral RNA, and then showed symptoms and RNA again later. These probably were continuing the same disease case, and were not re-infected. Follow-up found none transmitting to contacts (Korea Centers for Disease Control; Mandavilli “Can you get COVID-19 again?”).
Doing controlled tests on humans to discover how many developed immunity would be difficult and not-very-ethical, so scientists have been experimenting on animals who get COVID-19 similarly to humans, including hamsters (Chan, Zhang et al; Imai et al.; Sia et al.) and rhesus macaques (Chandrashekar et al; Deng, Bao et al.; Yu, Qi et al.) They found that some hamsters (Imai et al.) and rhesus macaques (Chandrashekar et al; Deng, Bao et al.) infected with COVID-19 developed antibodies and were protected against getting infected again.