Ordinarily, you can’t say much about the health of a staff member due to it being sensitive personal data, however the UK Information Commissioner has stated that you can tell other members of staff in these circumstances, provided you only go as far as necessary to safeguard the health and safety of others working with them.
The guidance states that “You should keep staff informed about cases in your organisation. Remember, you probably don’t need to name individuals and you shouldn’t provide more information than necessary. You have an obligation to ensure the health and safety of your employees, as well as a duty of care. Data protection doesn’t prevent you doing this.” The basic rule of thumb is that you should only tell the smallest possible number of people the minimum amount of personal information about someone else that is necessary to keep them safe.
More information from the ICO on data protection and COVID-19 can be found here.