Mathematical and hand wavy are not necessarily opposites, often there is a lot of hand waving involved in the assumptions that reduce the real world conditions

Mathematical and hand wavy are not necessarily opposites, often there is a lot of hand waving involved in the assumptions that reduce the real world conditions to the required conditions for the mathematical formula and that is certainly true when it comes to herd immunity. In particular treating R0 as a constant in the basic herd immunity equation is a huge leap to make.