Thread by @adamjkucharski

A few thoughts on the continued emergence of novel variants, and what it might mean for ongoing levels of COVID infection… 1/

https://twitter.com/theosanderson/status/1535222528414826496

As variants accumulate, it can be tricky to track combinations of past exposures (e.g. ), but to get some intuition, let's assume people simply get infected, build immunity, then gradually become susceptible to infection again (i.e. because variants). 2/ pubmed.ncbi.nlm.nih.gov/25800537/

If people become susceptible again rapidly, then we'll get new infections before the old ones have declined, and the level of infection will remain high. If it takes a while to become re-susceptible, then we'd expect gaps between epidemics and lower average infection levels. 3/

Using our (very) rough S ➡️ I ➡️ R ➡️ S process above, we can work out the level of infection (I*) corresponding to a given infectious period (d_inf) and duration of immunity (d_immunity). (Maths fans: this means solving for dI/dt = 0 if you fancy a puzzle.) 4/

It turns out this average level of infection is equal to: I* = (1-1/R0)/(1+d_immunity/d_inf), where R0 is the reproduction number if everyone were susceptible. If we assume people are infectious for about a week, we get the following picture: 5/

A couple of things jump out. First, once R0 is reasonably high, it's duration of immunity (i.e. rate of emergence of variants that evade immunity) that really drives average infection level, not the inherent transmissibility of those variants... 6/

Second, we've seen infection % in ONS data in the 2-8% range during 2022, with two new variants dominating in past six months (BA.1, BA.2), and new ones now growing (BA.4 & BA.5). So roughly consistent with above plot if people become susceptible again every 3-4 months or so. 7/

Throughout pandemic, discussions have often had a 'one more wave, then it's all done' framing, but above illustrates infection could down to quite high average level, depending on rate of variant emergence and tools countries develop to counter them (e.g. new vaccines). 8/8

Technical note: The above assumes loss of immunity is gradual and exponentially distributed, whereas reality will depend on emergence of variants. However, can construct alternative models to explore short-term dynamics as well as average infection level: epubs.siam.org/doi/abs/10.113…