Also, how exactly would you prove herd immunity when we don't know the antibody threshold required? We also don't know that antibodies are the primary mode of immunity- could be T cells. So I'm not sure what kind of analysis you are looking for.
[EDIT: For major amends. Mark it so it is clear that you made a change.]
I was only suggesting that you can edit your comments. Instead of posting two comments as replies, like here, you can edit your first comment and add the second part in the same comment.