The Gomes 'herd immunity' paper is, I believe, mathematically correct. I find it actually useful to conceptualise why 'pandemic waves' die out, well below classical 'herd immunity' thresholds and despite the presence of a large pool of susceptible hosts. (1/3) https://twitter.com/FrankDGonzo/status/1288922055774068736

It makes intuitive and mathematical sense that 'herd immunity' can be acquired with a small proportion of immunised hosts in a heterogeneous transmission network. In short, once the highly connected nodes in the network (hosts) are out (immunised/dead), the outbreak wanes. (2/3)

Though, I doubt such 'herd immunity' can be extended to successive waves. People are born, die, move between households/workplaces ... As such, the transmission network gets redrawn, and it requires only fairly minor rearrangements to be back essentially to square one. (3/3)