What happens when a population reaches herd immunity? Does it mean epidemics suddenly stop forever? Unfortunately not... 1/
The herd immunity threshold is when susceptibility is reduced to point where R=1, i.e. epidemic remains flat (the precise value of threshold can depend on population structure, e.g. quantamagazine.org/the-tricky-mat…). But even if this happens, R won't stay equal to 1... 2/
Over time, births will increase the proportion of the population susceptible. This will mean R>1, so we'd expect an outbreak in the (mostly young) susceptible group, which reduces R<1 again, with R=1 on average over time. In other words, the disease has become 'endemic'. 3/
This is why many endemic infections are diseases of childhood - for example, in populations that don't vaccinate again chickenpox, outbreaks occur among younger susceptible groups, who (in the case of infection with chickenpox virus VZV) then develop some immunity. 4/
The frequency of these outbreak-then-immunity cycles depends on transmissibility of the infection. In the Pacific, each dengue serotype typically causes outbreaks every 12-15 years (wwwnc.cdc.gov/eid/article/20…), which is what we'd expect from simple epidemic model including births 5/
Measles (before vaccination was introduced) was more contagious, and hence required fewer new susceptibles to cause outbreaks, so came back every year or two (journals.plos.org/ploscompbiol/a…). 6/ 
COVID cases are unfortunately rising in many countries, which means those populations will likely accumulate some immunity (although it's unclear how much, or how long it'll last). Clearly the hope is that, in longer term, a vaccine can reduce susceptibility everywhere. 7/
But it's worth bearing the above in mind when discussing long-term dynamics – even if susceptibility is reduced in the short-term, we shouldn't expect COVID to necessarily disappear indefinitely. 8/8
