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PRELIMINARY: Optimal Management of the COVID-19 Epidemic: When and How To Reopen the Economy?

by Carlos GarrigaRody Manuelli, and Sid Sanghi
Posted online May 13, 2020

As the numbers of infected cases and deaths associated with the COVID-19 epidemic begins to slow down or even decline, one of the most pressing and challenging issue is the reopening of the economy. Namely, policymakers and health officials must decide when to reopen the economy and how to respond if the number of infections, as a result of opening the economy, suddenly increases. These are hard questions to answer that depend on a multitude of factors, including the fundamentals and the current stage of the epidemic, as well as socioeconomic characteristics of the geographic area in question. In this post, we provide some lessons learned from an ongoing project on optimal policy during an epidemic.1

Our approach integrates a standard epidemiological framework with an economic model. This framework includes how the level of activity can be affected by a government that can impose restrictions along the lines of the mandated “stay at home” policies used in many countries. In addition, it includes the use of vaccination as a policy to contain the epidemic when a vaccine becomes available in the future. The benefit of reducing economic activity is a reduction of the rate of infection in the population, something that society values. The trade-off between the rate of economic activity and rate of infections determines the timing and the intensity of the optimal management of the pandemic.

To understand the policy prescriptions, it is important to provide some additional non-technical details about the problem. At the start of the epidemic, labeled as Phase I, the only policy tool available to manage the epidemic is employment restrictions. Keeping individuals at home instead of working reduces the rate at which susceptible individuals interact with infected individuals that are asymptomatic. These policies reduce the transmission of the virus at the expense of prolonging the duration of the epidemic, but make the epidemic last longer unless a vaccine is discovered.

If a vaccine is discovered, something that is outside the control of the government, the economy enters Phase II of the problem. A key assumption at this stage is that the vaccine can be used to control the virus by vaccinating susceptible individuals but cannot fully eradicate the disease. This possibility allows the long-run coexistence of a very small degree of recurrent cases of the disease in a population of susceptible individuals (i.e., as in the case of the flu) with full economic activity.2 The healthcare system is constrained by the hospital beds, and one of the key goals of the government is to minimize deaths  hospital capacity, thereby “flattening the curve,” with a fairly optimistic valuation of the economic contribution of each life lost.

The solution to the optimal management of the epidemic  provides guidance on when and how to reopen the economy. Our “when” in the question means the date the stay-at-home policies start to relax, and our “how” means the time it takes to bring economic production back to full capacity.3 Our quantitative predictions rely on standard estimates of the epidemiological parameters. It is necessary to mention that there is a significant degree of uncertainty about many of the key parameters—those corresponding to the economic model and those implicit in the epidemiological model. As better data and information become available, we can narrow down our estimates by identifying the most plausible scenarios.

Optimal management and the spread of the virus: It is useful to compare the evolution of the epidemic with and without intervention. As Figure 1 shows, in the absence of intervention (black line), the epidemic would peak at about 20 weeks and the number of infected people at that time would be 28%, exceeding the hospital capacity constraint as we have seen in some countries (i.e., Spain and Italy). In the baseline case (left panel of Figure 1), the vaccine is expected to be available to the public in 12 months, which is in line with the predictions of the Coalition for Epidemic Preparedness Innovation (CEPI). The arrival dates are represented by the vertical dashed line in each case. Under the optimal policy, the infectiousness curve is indeed flattened (red line), and it takes less than a year for the epidemic to peak (45 weeks), which is more than double the time in the absence of a policy. At the time of the peak, the share of infected population is 8.5%, which is exactly our estimate of hospital capacity, measured in terms of ICU beds, indicated by the blue dashed line. 

Figure 1: Time Path of the Infection: Uncontrolled and Optimal Management

Arrival Vaccine week 50                                                     Arrival Vaccine week 25

Source: Authors’ calculations.

Note: In both experiments, the expected discovery and distribution of the vaccine is 50 weeks.

We also analyze alternative scenarios, but the right panel of Figure 1 shows the case where the vaccine is discovered 6 months earlier than expected. In this case, the epidemic peaks in week 33, but the number of infections increases very rapidly when the vaccine becomes available. The differences in the spread of the epidemic are a result of the differences in stay-at-home policies and the availability of the vaccine. Figure 2 (left panel) depicts the optimal path relative to the full-employment case normalized to one. One should interpret the values in the vertical axis as measuring slack in the economy associated with the optimal policy. In response to the pandemic, the optimal policy prescribes an aggressive reduction in productive capacity close to 22% with a very gradual reopening 9 weeks after the initial case of infection.

At this point in time, the level of production is 35% below the pre-epidemic levels. It is important to emphasize that a gradual reopening occurs significantly before the peak of infections. This is consistent with the popular view that eliminating restrictions on business activity is associated with higher infections. This, however, is the optimal balance between the economic costs and managing the epidemic. In this baseline case, the arrival of a vaccine has no effect in terms of relaxing employment restrictions, as the economy is already operating at full capacity. However, if the vaccine arrives in week 25 instead of week 50 (see Figure 2’s right panel), then it is optimal to remove employment restrictions much more quickly.

The availability of a vaccine reduces the number of susceptible individuals, even when it is not feasible to vaccinate the entire population instantly, even with advanced healthcare infrastructure; and fewer susceptible individuals, even with a higher number of infected persons, results in a smaller spread of the epidemic.

Figure 2: Optimal Stay-at-Home Policy

Arrival Vaccine Week 50                                                    Arrival Vaccine Week 25

Source: Authors’ calculations.

We conduct a large number of additional experiments exploring alternative hypotheses, as well as sensitivity to different assumptions on key parameters. Below, we provide a streamlined summary of the main takeaways:

  1. Optimal and suboptimal management of the epidemic: The optimal policy depends on the numbers of both infected and susceptible individuals. Policies that wait until the peak of infections has passed are suboptimal, as the economy has to partially liberalize before the peak of infections. In general, it is extremely difficult to characterize the optimal policy, either in Phase I or II, relying exclusively on a decline in infections; but an implementation of the optimal policy requires random testing. Many other features of the environment—about which there is significant uncertainty—play a large role in determining the optimal policy. In general, optimal policies imply that a relaxation of stay-at-home restrictions will be accompanied by an increase in the spread of the virus.
  2. Infectiousness of COVID-19: How would the policy change if COVID-19 were found to be more infectious (with a reproduction number R0 of 4) than the current estimates with an R0 at 2.8? There is some suggestive research showing that the virus could be more infectious in areas with a high population density or in areas where most commuters use public transportation. With a higher initial rate of contagion, the optimal policy implies more stringent employment restrictions. In our analysis, the more aggressive optimal policy slightly reduces the long-run number of deaths averted when compared with the baseline case, but the economic loss is about twice as much.
  3. The timing of the arrival of the vaccine: Uncertainty about when a vaccine will become available plays a large role in determining the optimal policy. In our base case, the expected arrival of the vaccine is about 1 year. If a vaccine were to be available to the public 6 months before expected, it would cause an immediate return to almost full economic activity and a fairly large increase in the spread of the infection. The number of infections rises as a result of immediate liberalization of the stay-at-home rules before  declining as a result of a much steeper fall in the number of those susceptible to the virus (as a result of the vaccine). In this situation, the number of lives saved over the course of the epidemic is large, despite the fact that it is not possible to immunize everyone immediately, and the output cost is significantly smaller. When the vaccine arrival occurs beyond the expected years’ time—say, in 2 years—its impact on the optimal policy relative to the case with no vaccine is very small.
  4. Economic cost of the optimal management of the pandemic: In general, the economic cost of managing the pandemic is large and the economy remains below potential output for a long time. More specifically, the decrease in activity for the initial year ranges between 3% and 22%, with larger losses in the most pessimistic case. In most scenarios, the output cost per death averted exceeds $1.5 million and can be as high as $7.5 million dollars. However, we acknowledge that there is significant uncertainty about many of these key parameters, both those corresponding to the economic model and those implicit in the epidemiological model.
  5. Value of life and optimal policy: The valuation that society puts on human life (a very difficult subject) is critical in determining the optimal policy. For the cases described in this post, we assume that society cares only about the deaths due to exceeding hospital capacity, with a fairly optimistic valuation of the economic contribution of each life lost. In this post, we also consider a variety of scenarios, including one where “all lives matter,” which places an equal value on all deaths associated with the epidemic, which includes a fraction of all infected individuals and not just those dying due to exceeding the capacity of hospital infrastructure. This crucial aspect of the optimal policy is the discussed in a separate post.


1 The interested reader can access the technical version here: “Optimal Management of an Epidemic: Lockdown, Vaccine, and the Value of Life.

2 The possibility of a gradual roll-out of a vaccine makes the optimal management problem more challenging. The additional complexity has important implications for the policy choices in Phase I, when the vaccine is not available. Mainly because the government understands that, even with the vaccine, the epidemic cannot be immediately eradicated.

3 In an upcoming extension of this work, the optimal policy will provide the timeline of reopening of  so-called “non-essential sectors.” In the current analysis, the notion of openness is relative to full employment. 


Garriga, Carlos, Rodolfo Manuelli, and Sid Sanghi (2020). “Optimal Management of an Epidemic: Lockdown, Vaccine, and the Value of Life,” Working Paper Federal Reserve Bank of St. Louis.

Preliminary, incomplete. To cite, please request author’s permission.  

© 2020, Federal Reserve Bank of St. Louis. These views do not reflect the opinion of the Federal Reserve Bank of St. Louis or the Federal Reserve System. 

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