The importance of superspreaders in covid infectious waves

Summary: In this post I point out that the characteristics of covid waves don’t match that of a disease where every infected person goes on to infect others. Instead, covid infections appear to be more closely related to a superspreader model of disease propagation.

Way back at the beginning of the pandemic I recall seeing some modelling on how bad covid was going to get. It went something like this:

I don’t want to dwell on how badly wrong they got it all back then — it was a new disease and we really didn’t know how it would progress. The problem has been that exactly the same modelling fundamentals have been followed for more recent predictions that have been used to inform the decisions of government around the world.

The fundamental problem can be seen in the image above. There are four different scenarios presented in black, blue, brown and green, but each has a covid wave that only comes once. This was a fundamental of the Susceptible-Infected(Infectious)-Recovery (SIR) model in early 2020 — that once set in motion the disease would keep on infection susceptible people, that they’d become infectious and infect others, and that eventually a threshold of people would have been exposed (the herd immunity threshold) and the disease would go away.

In the months since early 2020 the SIR approach has been refined for covid, allowing for some waning of immunity and perhaps some seasonality (amazingly, not all covid models include seasonality effects even now) — but the fundamentals of SIR remain.

The trouble is, covid doesn’t appear to work this way:

• Each covid wave comes and then goes without infecting anywhere near the herd immunity threshold — the SIR model can’t readily explain why the disease wouldn’t continue to infect people. During 2020 this was explained away as being because of social and physical biocontrol measures (lockdowns, masks), but has time has progressed it has become clear that this just isn’t the case (eg, the covid wave structure is seen in countries that don’t adopt lockdowns). Even now, two years into the epidemic, in the UK only 22% people have the N-protein antibodies that signify natural infection with covid.

• Covid appears to be able to reach a rough plateau rather easily — continuing to infect around the same numbers of people every day for months on end (eg, in the UK from July to November). The SIR model doesn’t cope with this at all well — in SIR cases should either be increasing (there are more susceptible people to infect) or decreasing (enough people are recovered and no longer susceptible).

• Frankly, covid just doesn’t appear infectious enough to explain the SIR model. For example, according to UK HSA data in households with a coronavirus Delta-variant infection only 10% result in someone else in that household becoming infected with covid.

But we all know that this is how diseases work… if you’re susceptible then you get infected, possibly infect others during your infectious period, and then recover and usually have at least a period of protection from infection from the same pathogen, and possibly protection for life…

Enter Hope-Simpson.

Edgar Hope-Simpson was an expert on the way diseases spread who noticed in the 1950’s that influenza didn’t propagate as was expected by theory. As he explains in the opening page of one of his later papers on the spread of influenza¹:

None of this behaviour is explained by the current concept that the virus is surviving like measles virus by direct spread from the sick providing endless chains of human influenza A. A number of other aspects of the human host-influenza A virus relationship encountered in household outbreaks are among the list of 20 difficulties that are inexplicable by the current concept of direct spread.

Now, Hope-Simpson’s theory on the spread of influenza clearly isn’t directly applicable to covid — for a start covid is a coronavirus not an influenza, but, more importantly, his theory takes into account the fact that influenza outbreaks depend on immunity gained many decades previously (this obviously doesn’t apply to covid).

But there are important parallels that indicate that the SIR model is not applicable to covid either:

• Hope-Simpson notes that household secondary infection rates are surprisingly low for influenza, given the supposed R0 value for the disease — he notes secondary infection rates for influenza run at around 15% but considers that really secondary infection rates should be around 50-60% for a virus with its supposed virulence. I note that UKHSA estimates of secondary infection rates in households is approximately 10% (Delta) to 16% (Omicron) (see Table 4 of this document).

• Influenza outbreaks ‘run out’ long before the supply of potential susceptible individuals have been exhausted. Hope-Simpson notes that the 1957 influenza outbreak infected ‘only’ 15% of the potential susceptible individuals, but that the normal explanation (that there were more individuals with asymptomatic disease who gained immunity and thus removed the source of new susceptible individuals) couldn’t be true because there was a new influenza outbreak only 8 months later. The parallels for covid are clear — each covid wave only infects a small proportion of the population before extinguishing itself, but several months later a new covid wave appears.

• In other papers Hope-Simpson notes that challenge trials, where people are deliberately infected with influenza, produce rather few actual infections (the famous (and rather unethical) Deer Island influenza trials are the poster child for these, though I note there are many others that have shown similar results). This is very difficult to square with the supposed infectious nature of influenza. I note that while human challenge trials for covid have been started, none have reported any data as of now — this slow reporting is rather odd given that covid is supposed to be a terrible epidemic.

Given the data we have on covid outbreaks I suggest that some (not all) of Hope-Simpson’s model applies to covid as well. The key points of this hypothesis are:

• Covid is spread by superspreaders. The concept of superspreaders seemed to be accepted back in early 2020, but since those days not much has been mentioned about this. I suggest that the majority of cases are infected by a low number of superspreaders.

• In contrast, the non-superspreader infected individual only rarely spreads covid to others.

• Superspreaders catch covid some time before they become contagious, and remain contagious for longer than the normal infectious period.

• Each infectious wave stops when the supply of superspreaders runs out, not when the supply of susceptible people to infect runs out.

• New superspreaders are generated during each covid wave, who then have a latent/dormant infection until they become an active superspreader some time later.

• It isn’t clear if superspreaders only have one superspreader episode and each covid wave needs new individuals to become superspreaders, or if a given superspreader goes back into latent mode after their superspreading episode, and that after their period of latent infection they can become superspreaders again.

• Superspreaders have asymptomatic infection. They might have symptomatic disease after their superspreading episode, but when they are active they are asymptomatic (or possibly paucisymptomatic). It is the asymptomatic infection that allows them to infect many others while being unaware of their status (if they were symptomatic they would be likely to self-isolate).

In addition, the characteristics of covid outbreaks so far suggest that:

• Superspreaders make up between 1-5% of those susceptible to covid.

• Normal people go on to infect very few others — perhaps only one onward infection for every 7-10 infectious non-superspreader.

• Superspreaders infect many others — it is likely that each superspreader goes on to infect over 100 individuals.

• The latency period is between 1 and 6 months (more on this in a minute).

• Superspreaders remain active for approximately three weeks (I believe that they are superspreaders during asymptomatic infection, which eventually turns into a symptomatic infection and which point they overcome the virus).

• The young are much less likely to become a superspreader than those aged over 30.

Finally, I suggest that the vaccines have increased the likelihood of an individual becoming a superspreader and has decreased the time for the latent period (from approximately 4-6 months to approximately 1-2 months).

In my next post I will present data to support this hypothesis.

1. Even better, read his book — The Transmission of Epidemic Influenza.