I didn't assume that you did. Rather, I thought you were interested comparing kinds of immunity. To to that fairly and well, you need to include the most commo

I didn't assume that you did. Rather, I thought you were interested comparing kinds of immunity. To to that fairly and well, you need to include the most common case: People's first infection. Remember that most people's immune system is able to learn quickly enough that natural immunity takes care of the first infection without external help. The immune reaction doesn't start with the second infection, it starts as soon as the immune system starts learning. Excluding the first infection in an analysis seems very, very strange to me.