# Reinfection risk for Covid

### Are the 'reinfection rules' resulting in an apparent reduction in Covid infections?

We’re now well past the peak of infections for our latest Covid wave in the UK and well on the way to finding out what the inter-wave infection rate will be. My guess is that we’ll see around 125,000 new cases a day — similar to that seen before the latest wave.

One point about the Covid waves that’s important to note is that people seem to think that the proportion infected at the peak is the same as the proportion infected during the wave — about 7% of the population in the UK. Remember that this is just for the peak — there will be a substantial proportion of the population infected before this point but who recovered by the peak, and there will also be a significant proportion infected after the peak — I imagine that we will have seen around 20% of the UK population infected during this recent Covid wave.

But one aspect of this Covid wave remains relatively unexplored — the timing between Covid waves. This is seen most clearly in the Zoe symptom tracker data:

Note the dates of the peaks of the last two waves: 4th April and 17th July. This gives a period between the waves of 104 days — or exactly one fortnight more than 90 days.

90 days is important because it is the period defined by most bodies as the time where covid reinfection cannot occur — positive tests within this period are considered to be an echo of the original infection, even where new symptomatic disease occurs many weeks after symptoms originally stopped.

There’s surprisingly little data available on reinfections that isn’t complicated by this assumption that reinfection can’t occur within 90 days. For example, the latest ONS data on reinfections suggests the following risk profile:

Note the point where the risk goes to zero — 104 days after the prior infection. They’re definitely assuming that 90 days must pass before a new infection can occur (it is stated in the spreadsheet), but again there’s another 14 days added on. Is this the assumed duration of the infection?

It is also worth noting that the curve presented by the ONS above is for a strange individual — the risk is for:

a 60 year old male with no long-term health conditions, living in a 3 person household at median deprivation, working in a non-patient facing healthcare role, with a first infection Ct value of 20, 14-89 days after second dose of the vaccine and currently in the …Omicron variants dominant period (20 December 2021 onwards)…

That sounds like the risk is for an older male individual who has had their second dose of vaccine, but this isn’t the case — every point of the graph is for an individual within 90 days of having their second dose. Eg, for the point at 200 days post infection, the assumption is that they had their second dose of vaccine between day 110 and day 185 after their infection; for the point at 300 days post infection, the assumption is that they had their second dose of vaccine between day 210 and day 285 after their infection. The graph above might well be interesting from a scientific point of view, but it doesn’t actually offer information on the way risk might change with time for a real person.

Also note that their reinfection risk is for the Omicron period, yet their graph goes out to over two years after their first Omicron infection. The graph is clearly the result of a simple infection model set to a risk of zero at 104 days post infection.

So much for those ONS data.

To illustrate how complex this is, here’s an earlier graph of data produced by the ONS on reinfection risk, this time to summer ‘21:

For this graph the zero risk point is at exactly 95 days after the first infection — there is still the same assumption that reinfection cannot occur within 90 days of the first infection. I think that the profound difference in the shape of the reinfection risk graphs is entirely due to the strange definition in the more recent curve that vaccination had occurred within 90 days of each data point, whereas the older reinfection risk graph doesn’t have this restriction — are they trying to suggest in the more recent publications that reinfection risk is very low by ‘fiddling the books’?

I also note that the peak reinfection risk in this earlier data is only 122 days after the first infection — this is only 32 days longer than the assumed ‘zero risk’ period, and is enough in itself to suggest that the 90 day assumption should be challenged.

Nearly all scientific papers on reinfection risk use exactly the same restriction — that reinfection just cannot occur within 90 days of the first infection. There’s just one paper that I could find that didn’t have this restriction — a paper on reinfection severity based on US veteran medical data. This paper included the surprising finding that:

The median distribution of time between the first and second infection was 79 days (IQR: 48–119), and between the second and third was 65 (43–97).

Ie, this paper found that the most common period between a first infection and reinfection was only 79 days — 11 days under the period there reinfection is presumed by most bodies, including the UKHSA and ONS, to be impossible to occur. What’s more, further infections only reduced this period.

Thus there are indications that non-trivial numbers of reinfections have been occurring within the 90 day ‘zero risk’ period. This then leads to three obvious questions:

To what extent are official statements from the ONS and others on the Covid infection rate in the UK underestimating the problem?

To what extent does vaccination modify the reinfection rate within this 90 day period?

To what extent does the 90 day assumption of ‘zero risk’ influence the shape and timing of the Covid wave data?

It would be nice to see much more data on the reinfection risk during this period; I doubt that these data will be made available.

Here in the DC area (USA) people are getting infected left and right. I personally know of numerous people infected in the past few weeks. However, the official case numbers are at medium levels. This is because few people are getting PCR tested anymore. People are using home tests or not testing at all. It makes it pretty hard to track infection waves here due to the lack of reporting.

Australia followed the "no reinfection exists within 90 days" dogma for a while... they changed the reinfection period to be 28 days recently https://www.health.nsw.gov.au/news/Pages/20220712_00.aspx