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Smart lockdowns to control COVID-19

A dynamic model of SARS-CoV-2 transmission is integrated with a 63-sector economic model to identify control strategies for optimizing economic production while keeping schools and universities operational, and for constraining infections such that emergency hospital capacity is not exceeded.

The SARS-CoV-2 (COVID-19) pandemic raised the challenge of how to control its transmission when there were no known therapeutics or prophylactics. As a method of control, most countries used a combination of non-pharmaceutical interventions (NPI) such as the isolation of infected people, the tracking of exposed people, travel restrictions, and lockdowns, where most people stay at home. In general, Western countries did not have sufficient test-and-trace capacity to control the pandemic1,2,3. As a result, the blunt instrument of lockdowns was used to reduce contact between individuals to slow and control the spread of COVID-19 (ref. 4). However, a lockdown has economic consequences by disrupting the normal patterns of production and trade. The question for policy makers is how to balance the control of COVID-19 through NPIs while taking into account their economic costs. Writing in Nature Computational Science, David Haw and colleagues presented a model, called DAEDALUS, to study whether a nuanced approach of locking down only some sectors can control the pandemic in the short run at minimal economic loss5. The main purpose of the model is to guide practical policy making around these choices.

When it comes to the spread of an infectious disease such as COVID-19, differences in transmission must be taken into account. Different age groups have different patterns of interaction; for example, children largely interact with their parents and other children but not with other adults. Also, different environments have different patterns of interaction: in a workplace, the same people interact over a period of time and transmission will depend on the nature of work and density of the workplace6. Whether transmissions in a workplace will transmit outside depends on the extent of infections in the workplace as well as the interaction with the population. Some sectors have an interface with the public, such as hospitality and leisure, where there can be three types of onward transmission: between workers in the sector, from workers to their families and their contacts, and to the public who use the services of the industry. This sector also has younger workers on average who are more likely to be asymptomatic and thus, more likely to transmit infections as they are not easily identified as infectious7. On the other hand, abattoirs had very high transmission of the first and second kinds8 but will have low transmission of the third kind. Thus, from a public health perspective, a nuanced approach is needed to control transmission and it would seem desirable to close industries where the risk of subsequent infection is high, and which are ‘non-essential’ for the functioning of the economy.

This public health perspective has to be balanced with the economic consequences of closing some sectors. From an economic perspective, closing a particular sector will depend on its interconnectedness with other sectors as well as how important is it in terms of its contribution to GDP (gross domestic product). It turns out that the economics literature has generally not used sufficiently detailed modeling of the economy and contact structures to guide nuanced policy decisions, while the public health and epidemiology literature has not modeled economic costs. Denmark used a rudimentary model9 to guide their policy, but the UK did not. As a consequence, the UK introduced the ‘Eat out to help out’ scheme in 2020 to help restaurants and the hospitality sector by subsidizing eating in eligible venues, given the fear of business owners becoming bankrupt, and the fact that the income of workers in small and owner-run establishments were not adequately covered by other schemes developed to help those employed in larger firms. However, with the ‘Eat out to help out’ scheme, there was a notable increase in infections: the scheme contributed to 8–17% of all infections during that period, but without an appreciable increase in GDP10. A model that integrates both epidemiological and economic constraints in great detail is therefore needed.

In this sense, DAEDALUS5 is an important piece of applied policy work, marrying epidemiology and economic modeling. There are two components to DAEDALUS. The first is an age-structured SEIR model11, where the different age groups of the population have different risk characteristics (susceptibility) and different patterns of interaction (Fig. 1a). Each individual can be in one of four states: healthy and susceptible to COVID (state S); exposed to infection but not yet infectious and capable of transmitting the disease (state E); infectious (state I), in which the person can transmit the disease whether they are symptomatic or asymptomatic; and recovered from the disease and immune to subsequent infections (state R). A fraction of the symptomatic are hospitalized, and a fraction of these die from the disease. The second component to DAEDALUS is a detailed model of the economic production network to study the economic consequences of such interventions. This is done by using the input–output model12 introduced by the economics Nobel Prize winner, Wassily Leontief (Fig. 1b). It is a standard way of modeling interactions between different sectors of the economy. If we consider a simple scenario of two sectors — iron and coal — iron uses coal as an input but the output is also used in the production of coal. The same is true for coal, which uses iron as an input but the output of coal is used in production of iron. In this case, the interactions between the two sectors can be represented by a 2 × 2 matrix, A, where each cell aij represents the amount of input of sector i used by sector j. As it is a fixed matrix, it assumes that proportions of inputs used in production are fixed and there is no substitution between the two. This is valid in the very short run — perhaps a few months — and is used for detailed modeling of economies. Input–output tables are available for most economies.

Fig. 1: Integrating epidemiology and economic modeling.
figure 1

a, The SEIR epidemiology model. b, An example of the input–output economic model, where aij is the share of output of industry i used by industry j; for example, a12 is the share of agriculture output used in the telecommunications industry, which could be zero. c, The interaction between disease transmission and economic activity; places of infection are depicted in blue, the economic sector is depicted in green, and NPIs and lockdowns are depicted in pink.

The main contribution of DAEDALUS is to match the detailed input–output and epidemiology modeling, where the contact rates between different population groups are used at each industry level (Fig. 1c). From the input–output tables, the value added, which contributes to the GDP of each sector, can also be calculated. Thus, the combined model can be used to see how to maximize the GDP subject to production constraints given by the input–output table, dynamics of COVID-19, hospital capacity, constraint that the pandemic is controlled — represented by requiring that the reproduction number at the end of intervention is Rend ≤ 1 — and other desirable objectives such as keeping the schools open. The problem reduces to a programming problem where some constraints are non-convex due to the disease dynamics13.

The model is flexible and can be tailored to fit different economies and to reflect different epidemiology assumptions as these may also vary across countries. As an example, the UK was modeled with 63 economic sectors, worker-to-worker contact rates were based on French data, and the epidemiology parameters were calibrated on UK data. Different scenarios were simulated. For instance, it was projected that, with a smart lockdown, there could be a gain of 24–29% over six months compared to a blanket lockdown of all non-essential activity. Sectors that are either ‘essential’ for the working of the economy or high value-added, but where risk of onward transmission is considered low, should be allowed to operate.

The proposed model is an important step for integrating epidemiology and economic modeling and there is room for extending it. The available hospital capacity is important for determining the extent of lockdowns. One could, in principle, determine the shadow value of an additional hospital bed, which is the increase in the value of maximized objective — in this case GDP — of marginally relaxing the constraint of number of beds. The shadow price of relaxing other constraints can also be estimated, which would be valuable to plan for future outbreaks of COVID-19 or other pandemics. Infections lead to mortality both directly and indirectly due to channeling of medical resources to deal with COVID-19. Mortality is a big driver of policy response. Therefore, the objective should be extended to include mortality14, as this will give a more complete picture of the trade-offs involved in practical policy making.


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Correspondence to Aditya Goenka or Lin Liu.

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Goenka, A., Liu, L. Smart lockdowns to control COVID-19. Nat Comput Sci 2, 217–218 (2022).

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