Thread by @gro_tsen

One thing I forgot to illustrate in the numerical experiments quoted below is the sort of things which can happen if there is more heterogeneity in the susceptibility of the variant than of the ancestral strain. So let me add this new set of graphs and explanations. ⤵️ •1/14

https://twitter.com/gro_tsen/status/1367925767854841857

The color code and layout of graphs still follow the same conventions, explained in a couple of tweets after the one quoted below. But let me explain what I did here. •2/14

https://twitter.com/gro_tsen/status/1367925780165058560

Generally speaking, the effect of heterogeneous susceptibility (for a single strain) is that more susceptible individuals become infected, and thus immune, earlier on than less susceptible ones, so as immunity accumulates two things happen at once: … •3/14

… one is that fewer individuals are susceptible at all, but the other is that even those who are are among those who were less susceptible at the start. So the overall effect is that immunity slows the epidemic more effectively than for a homogeneous population. •4/14

Now my set of graphs, requoted below, showed what happens when two pathogen forms, one starting with R=1.0 and the other with R=1.4, with cross-immunity between them, compete for the same population: … •5/14

https://twitter.com/gro_tsen/status/1367925767854841857

… either in a homogeneous population (everyone has the same susceptibility to both strains) … •6/14

https://twitter.com/gro_tsen/status/1367925790449541128

… or on a heterogeneous one where susceptibility follows a (fairly natural) exponential distribution for both strains. •7/14

https://twitter.com/gro_tsen/status/1367925796367654927

But in both of these cases the distribution of susceptibility to both pathogen forms was the same (either homogeneous = concentrated at one value, or heterogeneous in the form of an exponential distribution). What if the two differ? •8/14

Well this opens a whole can of worms because we need to decide not just how the two susceptibilities are distributed separately but also how they correlate. In the above they were perfectly correlated, but now we have a bazillion things we can do. •9/14

So I did something fairly simple: the ancestral form has constant susceptibility (no heterogeneity), while the variant has heterogeneity, which I made more pronounced (Γ-distributed with shape ½ rather than 1 [exponential]). •10/14

The other conditions are left exactly as they were in my initial experiments, such as the initial conditions. •11/14

https://twitter.com/gro_tsen/status/1367925773282185224

The result is as follows (same image as in the first tweet of this thread): the bottom line is that, while the variant is more contagious, it tends more strongly to infect people who are more susceptible to it, reducing its own advantage. •12/14

So we see (what follows is a zoom on the graph of reproduction numbers: purple is for the variant, beige is for the ancestral form, and black is overall) the variant's “advantage” drop as immunity is accumulated by the variant (but not by the ancestral form!). •13/14

For those who want to play with this, the code is here: gist.github.com/Gro-Tsen/4eacb… (run it with `hetcoefx2=2.0` to reproduce the behavior illustrated here). •14/14