Reaching Herd Immunity Far Earlier than Expected

Timothy Birdnow

Herd immunity is going to be reached much earlier than thought.

From Judith Curry's blog:

The ‘herd immunity threshold’ (HIT) can be estimated from the basic reproduction rate of the epidemic, R₀– a measure of how many people, on average, each infected individual infects. Standard simple compartmental models of epidemic growth imply that the HIT equals {1 – 1/R₀}. Once the HIT is passed, the rate of new infections starts to decline, which should ensure that health systems will not thereafter be overwhelmed and makes it more practicable to take steps to eliminate the disease.

However, the Ferguson20 report estimated that relying on herd immunity would result in 81% of the UK and US populations becoming infected during the epidemic, mainly over a two-month period, based on an R₀ estimate of 2.4. These figures imply that the HIT is between 50% and 60%.[2]Their report implied that health systems would be overwhelmed, resulting in far more deaths. It claimed that only draconian government interventions could prevent this occurring. Such interventions were rapidly implemented in the UK, in most states of the US, and in various other countries, via highly disruptive and restrictive enforced ‘lockdowns’.

A notable exception was Sweden, which has continued to pursue a herd immunity-based strategy, relying on relatively modest social distancing policies. The Imperial College team estimated that, after those policies were introduced in mid-March, R₀ in Sweden was 2.5, with only a 2.5% probability that it was under 1.5.[3] The rapid spread of COVID-19 in the country in the second half of March suggests that R₀ is unlikely to have been significantly under 2.0.[4]

Very sensibly, the Swedish public health authority has surveyed the prevalence of infections by the SARS-COV-2 virus in Stockholm County, the earliest in Sweden hit by COVID-19. They thereby estimated that 17% of the population would have been infected by 11 April, rising to 25% by 1 May 2020.[5] Yet recorded new cases had stopped increasing by 11 April (Figure 1), as had net hospital admissions,[6]and both measures have fallen significantly since. That pattern indicates that the HIT had been reached by 11April, at which point only 17% of the population appear to have been infected.

How can it be true that the HIT has been reached in Stockholm County with only about 17% of the population having been infected, while an R₀ of 2.0 is normally taken to imply a HIT of 50%?

A recent paper (Gomes et al.[7]) provides the answer. It shows that variation between individuals in their susceptibility to infection and their propensity to infect others can cause the HIT to be much lower than it is in a homogeneous population. Standard simple compartmental epidemic models take no account of such variability. And the model used in the Ferguson20 study, while much more complex, appears only to take into account inhomogeneity arising from a very limited set of factors – notably geographic separation from other individuals and household size – with only a modest resulting impact on the growth of the epidemic.[8]Using a compartmental model modified to take such variability into account, with co-variability between susceptibility and infectivity arguably handled in a more realistic way than by Gomes et al., I confirm their finding that the HIT is indeed reached at a much lower level than when the population is homogeneous. That would explain why the HIT appears to have been passed in Stockholm by mid April. The same seems likely to be the case in other major cities and regions that have been badly affected by COVID-19.

Posted by: Timothy Birdnow at 07:23 AM | No Comments | Add Comment
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