Let me see if I can use some basic epidemiology to independently estimate the order of magnitude of the duration of immunity in the endemic human coronaviruses like HCoV-OC43. •1/12
As a reminder, there are four known endemic human coronavirus species: OC43, 229E, NL63, HKU1 (and probably more that aren't known), causing cold-like symptoms. The first two appear to be the most frequent. See this mini-thread: •2/12
Let me use a very basic epidemiological model: SIR with processes S+I→I+I (infection), I→R (recovery) and R→S (loss of immunity) having first-order kinetics with constants β,γ,δ respectively. And assume a steady state: … •3/12
… so, denoting s,i,r the proportions of the population that is susceptible, infectious and immune respectively, we have: β·i·s = γ·i = δ·r during this steady state. With s+i+r=1 this solves to: s = γ/β and i = ((β−γ)δ)/(β(γ+δ)) and r = ((β−γ)γ)/(β(γ+δ)). •4/12
Now what is known? Well, from the paper medrxiv.org/content/10.110… estimating their epidemiological parameters (table 1 on page 2), I find 1/γ (infectious period) ~ 15d and β/γ (reproduction number) ~ 4. What I care about is 1/δ (duration of immunity). •5/12
To estimate δ, let me estimate i: well, Wikipedia suggests (with a reference, but I couldn't check it) that the frequency of common colds is about 2 to 4 per year in adult. Let's put it at 3/yr. •6/12
How many of these are caused by coronaviruses? I've seen a number of sources say between 10% to 30%. I was unable to track down a precise reference. Let me say 15%, roughly the geometric mean between the two, to get an order of magnitude. •7/12
So it seems that we're infected by a human coronavirus approximately once every two years. Now I have no idea how frequent each of OC43, 229E, NL63, HKU1 are, but the first two probably make up the larger share since they were discovered long before the other two. •8/12
So let's say that OC43 makes up around 40% of infections caused by human coronaviruses: this means we get it once every 5 years. And since average duration 1/γ (see above) is 2 weeks, we have i ~ 1/130. •9/12
Solving for δ (using the expression i = (1−γ/β) / (1+γ/δ) gives 1/δ ~ 190week or 3½ years of immunity. This is all wildly inaccurate, of course, and shouldn't be taken as more than an order of magnitude! (And the model itself is highly simplistic.) •10/12
But it certainly suggests that immunity to endemic human coronaviruses must last at least a year or two, or we would be getting more colds (or at least more coronavirus-caused colds) than we do, providing independent confirmation of the estimate in the paper from tweet 1. •11/12
Also, if their reproduction number is about 4, at any given point in time, about 3/4 of the human population should be immune to each one of these HCoV's. So the idea that they might play a part in SARS-CoV-2 immunity isn't nonsensical from that perspective. •12/12
