Herd immunity is a term that has risen in public consciousness as a long-term solution for dealing with the COVID-19 pandemic. Read on to find out why this deceptively simple idea is not as easy to reach as it seems.
The idea of herd immunity is quite simple and has been known to epidemiologists for almost a century.[1] Once enough people develop immunity to a virus, there won't be enough new people for the virus to infect, causing it to eventually die out. The difficulty arises in both estimating this "herd immunity threshold" and subsequently developing immunity in enough people.
At first glance calculating the threshold seems straightforward. If every infected person infects R0 people on an average then the incidence of disease will begin to decline once more than 1 - 1/ R0 people develop immunity. For example, for a disease with R0 = 4, each infected person passes on the infection to 4 others. The incidence of disease will decline once more than 1 – ¼ = ¾ fraction of the population, that is, more than 75% of the population develops immunity to the disease.[2][3][4]
In part B of the figure, as the number of immune people is 75%, i.e., equal to the threshold, the incidence of disease remains constant. Every infected person passes on the disease to one new person. Clearly, if more than 75% of the population were to be immune, the spread of the disease would slow and from a theoretical perspective, stop altogether.
Though this simple model illustrates the idea of herd immunity, achieving this in practice is very challenging. The classical model assumes a homogeneity of population with all individuals being equally susceptible to the disease and also equally infectious. However for a global pandemic we simply cannot make these assumptions as there are large differences in people’s social behaviour, economic status, pre-existing health and work conditions which all significantly impact their susceptibility to the disease and their infectiousness. As a result, estimates of a worldwide R0 can be very inaccurate. This is the problem of population heterogeneity.[5]
SARS-CoV-2, the virus that has caused the covid-19 pandemic has an estimated R0 of 2.63 as a worldwide average when assuming a homogeneous population.[6] However due to population heterogeneity, these estimates vary over a large range for different regions of the world. With an R0 of 2.63, using the classical model the “herd immunity threshold” would be ~62%. Amongst the many gloomy realities caused by this pandemic, a glimmer of hope can come from the fact that most experts estimate the actual “herd immunity threshold” to be much lower than this ~62% due to the effects of population heterogeneity. Recent research which takes into account age cohorts and social activity reduces this threshold to 43%.[7] While the authors themselves admit that their model should be used as an illustration of the concept rather than a hard figure, more realistic and complex models have the effect of reducing the threshold even further. This is because in high contact environments such as metropolitan schools and workplaces immunity is concentrated among more active individuals. However, despite these promising figures there is still a long road ahead in the global fight against the pandemic.
Whatever the threshold may be, herd immunity is achieved through either natural infection or vaccination. The natural infection route is dangerous to rely upon not only due to the inevitable loss of lives but also because it is unclear whether infection with covid-19 actually develops immunity to the disease. Although it was initially thought that infection to covid-19 provides immunity, recently scientists have observed secondary episodes of acute, confirmed coronavirus symptoms in cured patients.[8] It is safe to assume that the fastest, reliable way to achieve immunity and beat this pandemic is an effective and safe vaccine.
Author: Daattavya Aggarwal, MSc. Mathematical and Theoretical Physics, Wolfson College, University of Oxford
References:
1. WWC, Wilson GS. The spread of bacterial infection: the problem of herd immunity. J Hyg1923; 21:243–9
2. Fine P., Eames K., Heymann L. D., “Herd Immunity”: A Rough Guide, Clinical Infectious Diseases, 52, 7 (2011), pp. 911–916
3. Smith CEG. Prospects of the control of disease. Proc Roy Soc Med 1970; 63:1181–90
4. Dietz K. Transmission and control of arbovirus diseases. In: Ludwig D, Cooke KL, eds. Epidemiology. Philadelphia PA: Society for Industrial and Applied Mathematics, 1975: 104–21.
5. Boylan D. Ross, A note on epidemics in heterogeneous populations. Math. Biosci., 105 (1991), pp. 133-1337
6. Mahase E. Covid-19: What is the R number? BMJ 2020;369:m1891
7. Britton T., Ball F., Trapman E. A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS-CoV-2. Science 369, 846-849 (2020)
8. Gousseff, Marie et al. Clinical recurrences of COVID-19 symptoms after recovery: Viral relapse, reinfection or inflammatory rebound?. The Journal of infection, S0163-4453(20)30454-0. 30 Jun. 2020, doi:10.1016/j.jinf.2020.06.073