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Lockdown by Algorithm: A Proposed Model Calculates Optimal Restriction Levels

Lockdown by Algorithm: A Proposed Model Calculates Optimal Restriction Levels

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During the pandemic, countries have endeavoured to protect their citizens without hurting their economies with excessive restrictions. At the seminar ‘Living with Covid-19: Optimal Lockdown Policies’, Hubert Kempf, academic supervisor of HSE University’s International Laboratory for Macroeconomic Analysis, presented a mathematical model that can be used to calculate the optimal level of restrictions.  

In 2020, many governments had to decide how to deal with the coronavirus pandemic, and the measures adopted varied greatly, depending on the severity of the epidemic in a particular country, its geographical location, the strength of its links to neighbouring countries, the political regime, and the views of the leadership. The severity of these measures ranged from complete lockdown, the halting of certain businesses, the closure of shops and cafes, and travel bans, to monitoring the situation without any restrictions.

Hubert Kempf
Photo courtesy of Hubert Kempf

Proponents of both extremes argue in favour of their preferred solution. Those who think it is appropriate to introduce a lockdown justify it on the basis of the need to contain the spread of the virus and to prevent the number of sick people from overwhelming hospital capacity. Those who oppose the restrictions point to the damage to the economy: entire industries (e.g., tourism and air travel) and many small- and medium-sized enterprises, which find it more difficult to survive a work stoppage than large ones, will suffer from a lockdown. In the first case, more people will be able to receive quality medical care and the death rate will be lower; in the second case, high unemployment will be avoided, and the severity of the economic crisis will be reduced.

Most countries have chosen policies that fall between these extremes. ‘Life during the coronavirus pandemic is a balancing act between the health benefits of lockdown and social distancing, and the economic and political costs of restrictions,’ said Hubert Kempf. But how can the severity of restrictions be calculated so that both public health and the economy suffer as little damage as possible? What are the parameters that determine economic damage and mortality rates?

It is not easy to generate a robust mathematical model, as the key factor (spread of infection) is not economic in nature and operates according to different laws. In addition, this pandemic represents the first time the global community has reacted in this way (never before have governments imposed such sweeping restrictions to save lives) and there is nothing to compare its evolution with. Several papers have been published on the course of Covid and the results of restrictive measures in different countries, but they do not offer mechanisms to guide decision-making processes.

Hubert Kempf and his co-author, Stéphane Rossignol of the University of Paris VIII, based their algorithm on the simple SIR model proposed by William Kermack and Anderson McKendrick in 1927. It divides the population into three groups: those who are susceptible, those who are infected, and those who have recovered. The model describes infection rates in a simplified way (a visualisation of the SIR model was made in the Washington Post).

Using existing work, the scientists created a mathematical model that takes into account the prevalence rate, R0 (the average number of people infected by one person who is sick), mortality (the proportion of those who become infected who die from the disease) and patient recovery. In addition, health system capacity (the number of people who can be treated at the same time) and the date at which a vaccine becomes available can be entered. The model calculates the duration of the pandemic, the damage to the economy, and the likely number of deaths associated with various levels of restrictions.

A key variable in the calculations is what the authors define as the ‘economic value of life'

This variable is assigned different values by different governments and determines the weighting with which the total number of deaths caused by the virus is included in the final equation. The equation itself allows for the calculation of an acceptable prevalence rate, and subsequently how stringent the required measures need to be to keep it at that level. In general, the higher a government values human life, the stricter the measures it takes should be, but for some ‘value of life’ ranges, the optimal level of restriction remains constant.

‘This work is theoretical; we are not trying to decide which policy would be right for Russia, for example,’ Professor Kempf said. ‘We want to understand how theoretically to justify mitigation policies.’

The International Laboratory for Macroeconomic Analysis was established in 2006. Its main areas of research are fiscal and monetary policy, the political economy of economic growth, and econometric methods of macroeconomic analysis and forecasting. Current laboratory projects include ‘Sustainable Public Finance’, ‘Information and Macroeconomic Policy’, ‘Problems in Empirical Macroeconomics and Macroeconomic Forecasting’ and ‘Political Economy of Growth and Development’. Twice a month the laboratory hosts an open research seminar. It is chaired by the Dean of the Faculty of Economic Sciences Professor Sergey Pekarski, and supervised by Professor Hubert Kempf (who is also Professor of Economics at the Ecole Normale Supérieure Paris-Saclay).

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