Interesting, it seems that different immune responses are possible:
https://www.immunology.org/news/immunity-and-covid-19-what-do-we-know-so-far
Does everyone make the same immune response to SARS-CoV-2?
No. The immune response varies hugely between different people. Some people create a very effective immune response, so they will not get sick again from SARS-CoV-2 and will not pass the virus to anyone else. Others will make antibodies and be protected from getting sick with COVID-19 but may still be infected with the SARS-CoV-2 virus and transmit it to others. Most people who are infected with SARS-CoV-2 make some form of immune response but whether this is effective at preventing reinfection in the future is not easy to determine.
We need to identity which immune markers (antibodies, T cells etc.) predict who is immune to COVID-19 and who is susceptible to either mild or severe disease. These markers will allow us to identify people who are at particular risk.
Are there any other factors that will have an impact on the level of immunity generated?
There are many factors that have an impact on the level of immunity generated, including age. Older people are less likely to make effective immune responses to infection, while there is evidence that children have a reduced antibody response to SARS-CoV-2.
Additionally, those people with weakened immune systems because of certain diseases or medication, will not be able to make as good an immune response as young healthy people.
How long does immunity to SARS-CoV-2 last?
As SARS-CoV-2 has only been around for a year, it is difficult to fully understand how long immunity lasts after infection. Current evidence suggests that antibody concentrations in the blood of people who have been infected do decline over time but can persist in some people for at least 8 months, and possibly longer, after infection. It has also been found that B and T cells that recognise SARS-CoV-2 are also present in the blood 8 months after infection. Exactly how long immunity will last will need a longer time to be determined but research into this is ongoing. For this reason, we do not yet know enough about the duration of protection to issue ‘immunity passports’.