This is an article by Martin Sewell. Martin is a quantitative researcher and developer in the financial industry. He can be contacted on firstname.lastname@example.org.
When a pandemic such as COVID-19 strikes, there are benefits to reducing the rate of infection. Doing so allows us to reduce the total number of people who get infected (minimise the overshoot), reduce the peak number of infections (so that healthcare resources do not become overwhelmed) and buy ourselves time (to prepare generally and hopefully develop a vaccine).
One obvious means of reducing the rate of infection is social distancing. People will tend to voluntarily reduce social interactions as they wish to reduce the risk of becoming infected. However, if they become infected themselves they will likely fail to internalise the costs they impose on others. For this reason, overall social welfare may be best served by government nonpharmaceutical interventions, such as a lockdown. However, a government’s job is to maximise the aggregate utility of the population over time, and a lockdown, like most policies, should be justified by a cost–benefit analysis.
I shall attempt a cost–benefit analysis of the UK lockdown. The National Institute for Health and Care Excellence (NICE) values a quality-adjusted life-year (QALY) at £20,000 to £30,000 in order to inform decisions that affect the allocation of NHS resources (NICE, 2012). For our calculations we’ll take the average and use £25,000. Of course this is not the same as the intrinsic value one puts on their own life or the life of a family member. Of the deaths due to COVID-19 occurring in April 2020 in England and Wales, 64% were male and 36% female (ONS, 2020). The average years of life lost, after adjusting for number and type of long-term conditions as well as age, for men was 13.1 and for women was 10.5 (Hanlon et al., 2020). So the average number of adjusted life years lost was 12.2 and the average value of life lost due to COVID-19 was £304,000 per person.
According to the Centre for Economics and Business Research (Cebr), at its peak the coronavirus lockdown was costing the UK economy £2.4 billion every day (Hymas, 2020). We can deduce that the lockdown was worthwhile if, and only if, it saved at least 7891 lives per day. The daily number of COVID-19 deaths in England peaked on 8 April 2020 at 801 (Leon, Jarvis, Johnson, Smeeth, & Shkolnikov, 2020), assume 966 for the whole of the UK. Therefore the UK lockdown was worthwhile if, and only if, it reduced the peak number of daily deaths by about 90%.
I reviewed the relevant literature on lockdowns, and for each article I estimated the number of deaths that would occur per day at the peak of the epidemic during a lockdown, relative to the number of deaths in the unmitigated case (Table 1). If we assume that the number of deaths in the unmitigated case is 100, the median number of deaths under a lockdown is 56. If we ignore articles not listed by Google Scholar, the median is 52. Whilst if we also ignore all articles with zero citations, the median is 49. In other words, at the peak of the coronavirus epidemic a lockdown reduces the number of deaths per day by approximately 50%.
In summary, it was estimated that a lockdown reduces peak daily deaths by about 50%, whilst the cost of the UK lockdown implies that it was only worthwhile if it reduced the death rate by about 90%. In conclusion, the UK lockdown was not justified.
Table 1: A literature review with estimates of the number of deaths per day during a lockdown at the peak of the epidemic, relative to the number of deaths in the unmitigated case (assumed to be 100).
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