## Introduction

According to the Bureau of Labor Statistics, the US unemployment rate in October 2020 stood at 6.9% and the number of unemployed at 11.1 million. This is likely an underestimated number since it does not include individuals who have stopped looking for employment1 due to poor economic prospects. Even though both measures have declined for 6 months consecutively, the unemployment rate is still higher by  3.5% and the number of unemployed by 5.3 million, compared to pre COVID-19 levels in February 2020. The US economy shrank by an annual rate of 4.8% in the first quarter of 2020 and by a shocking 32.9% in the second quarter, which has been the largest drop seen since 1945. The number of COVID-19 cases have crossed 12 million and number of deaths over 258,000 in November 20202.

This research builds a comprehensive system that combines the epidemiological model developed to study the spread of COVID-19 with a detailed model of the US economy to understand a sector wise economic impact from a shock to labor supply caused by the pandemic. Note that the focus of this paper is only on the shock encountered by the economic sectors from the supply side, and not on the demand side which has also dropped due to the high unemployment rate and a bleak economic outlook. We consider a number of counterfactual scenarios that comprise of various social distancing measures such as the stay-home order, voluntary home isolation of the symptomatic individuals, and school closure. We measure economic losses from the drop in labor supply in each sector due to the stay-home order, absenteeism due to illness and deaths, cascading loss to/from other sectors due to interdependencies between sectors, and the economic burden caused by the medical treatment of the infected. We vary compliance to interventions and duration of the stay-home order to determine their impact on economic and epidemiological outcomes and the trade-offs between them.

This research is an extension of the work done in3 which only focused on estimating the medical cost of treatment for COVID-19 cases under the same mitigation scenarios and the disease model. Here we calculate overall economic losses from a societal perspective which include the medical cost of illness, cost of intervention or social distancing i.e. healthy individuals unable to go to work, direct loss in productivity due to morbidity and mortality of workers, and the indirect loss caused by the interdependencies between sectors. We also estimate the effect of intervention scenarios on cases and deaths averted in the US.

This level of detailed analysis has not been done in the literature before for COVID-19, and can provide guidance to public health officials for developing strategies to balance the emergence of infections and deaths with the economic costs of the social distancing strategies. A longer duration of stay-home order causes economic losses even after accounting for telework, but it also significantly reduces infections and deaths, and losses caused by the medical treatment of the infected.

## Related work

There have been several papers that study the economic impact of COVID-19. Eichenbaum et al.4 study the interaction between economic decisions and epidemic outcomes and find that the competitive equilibrium is not socially optimal because infected people do not fully internalize the effect of their economic decisions on the spread of the virus. Their results show that an optimal containment strategy that starts early and ramps up with infections, can cause a large recession but save about half a million lives, assuming no treatment or vaccines are available. A counterfactual scenario analysis in5 shows that a delay of 4 weeks in applying control measures would have slowed the decay of the epidemic by 49 days in China. Work by6 shows that strict control measures in China led to a steep drop in the temporal effective reproduction number, a metric used for assessing the efficacy of interventions.

Work by7 shows that differential targeting of risk/age groups outperform uniform social distancing policies. Most of the economic gains in this study are realized from implementing stricter lockdown policies on the oldest age group. However a fully targeted policy can be challenging to implement and ethically questionable. Baker et al.8 characterize the uncertainty using stock market volatility measures, newspaper-based measures of uncertainty and survey-based perceptions of business level uncertainty; and find that more than half of the contraction in US economy is caused by COVID-induced uncertainty.

Toda (2020)9 uses an SIR model to study the impact of the epidemic on the stock market. Jones et al.10 use an SIR contagion model and a model for consumption and production to analyze optimal mitigation policies and interactions between economic activity and epidemic dynamics. They discuss congestion externality i.e. when hospital capacity is exceeded, the risk of death becomes higher but agents do not internalize the impact of their decisions on others and therefore behave in a socially sub-optimal way. Other papers that study the economic impact of COVID-19 and pandemics are11,12,13,14.

The ripple effects of pandemics across a regional economy are studied using an input–output model in15,16. The impacts of pandemic-induced workforce disruptions are assessed using economic losses as well as inoperability, which measures the extent to which sectors are unable to produce their ideal level of output.

The novelty of our research lies in building a detailed integrated system that combines a network based population model with an epidemiological model and an economic model. The disease spreads on the social network, as determined by the COVID-19 disease model; non-pharmaceutical interventions remove particular edges in the social network depending upon the type of interventions and compliance rate; the duration of the interventions determine the length of the time edges are removed for; the outcome of the spread is captured in terms of infections and deaths, which determine the shock to labor-supply in specific economic sectors, as determined by the occupation of individuals who are sick or dead, as well as those who are healthy but unable to work due to a lockdown. These shocks as well as the interdependencies between the sectors determine the sectoral and overall economic impact.

## Data and methods

This research integrates a variety of datasets to build a comprehensive model that includes individuals, their interactions, their health states over time as the disease spreads over the social contact network, their behaviors in terms of compliance with interventions and its effect on their health states, and the impact of their health outcomes on each economic sectors’ labor supply and hence sectors’ output. These datasets include, but are not limited to, demographics data from the US Census, daily activity data from American Time Use Survey, travel data from National Household Travel Survey, location data from Open Street Maps, disease model parameters from the US Centers for Disease Control and Prevention, medical costs from Kaiser Family Foundation, data on dependencies between industries from the US Bureau of Economic Analysis, and telecommunting data from17. Further details on how these datasets and other data are used in our models are given in the subsections below. Figure 1 shows the overall systems level architecture of the modeling framework, its various components and how they are linked together. Below we describe the various models used in this framework and how they have been synthesized to build an integrated system.

### Social contact networks

We use a synthetic social contact network generated using the methodology provided in18,19,20 and used in3,21,22,23,24,25,26,27 to study the spread of COVID-19. The social contact network is constructed using a first-principles approach that integrates various commercial and open databases through the following 4 steps. Step 1 constructs a synthetic population of the US by using datasetssuch as the US census block group level distribution data and Public Use Microdata Sample (PUMS) data. Step 2 assigns daily activities to individuals within each household using activity and time-use surveys (American Time Use Survey data and National Household Travel Survey Data). Step 3 assigns a geo-location to each activity that each person performs. The geolocations are based on data from Dun and BradStreet, land-use, Open Street Maps etc. Step 4 constructs a dynamic social bipartite visitation network, when people visit locations for performing activities. A dynamic social contact network is obtained from the colocation of individuals, where nodes are individuals and edges are the contact times. These types of networks have been validated and used to study various infectious diseases, interventions, and public health policy questions. For details on these studies and on the methodology to generate synthetic social contact networks, see19,20,21,23,28,29,30,31.

Each individual in the social network is endowed with a list of demographic attributes such as age, gender, income, occupation, family size, family income etc. consistent with the data provided by the US Census. A person’s occupation and the associated sector to which the occupation is linked, along with the health state (susceptible, infected or dead) of the person, are used to determine the sector level interruption in labor supply on any day that arises from sickness, mortality or stay-home order. This is the critical piece that joins the disease model with the economic model.

### Disease model

The disease model is the best guess version of “COVID-19 Pandemic Planning Scenarios” prepared by the US Centers for Disease Control and Prevention (CDC) SARS-CoV-2 Modeling Team32. It is an SEIR (Susceptible-Exposed-Infectious-Recovered/Dead) model where each individual at any given time is in one of these health states. Everyone starts in the susceptible health state except for the seed nodes who begin in the infected state. Once a susceptible person is exposed to the disease, s/he stays in the exposed state for the incubation period. After that, they move to infectious state. The infected individuals are further divided into presymptomatic, asymptomatic, and symptomatic health states. Only the symptomatic individuals may seek medical care and some of them may become hospitalized while others recover. The hospitalized individuals may further need to be on ventilators. The final health state of the infected is either recovered or dead.

The disease states and transition paths are shown in Fig. 2. The final disease state can be reached through multiple paths. The transition probabilities for each health state are shown in the Supplemental Information. The model is also age stratified for the following categories i.e. preschool (0–4 years), students (5–17) adults (18–49), older adults (50–64) and seniors (65+) and calibrated for each of the age groups separately. We use the disease model parameters as given by the CDC and do not analyze the sensitivities of disease model parameters to infections and deaths since our focus here is on understanding the effect of interventions and the parameters associated with interventions. The number of deaths simply depend on the number of infections. Age stratified probabilities of death are assigned to infected individuals at different stages of their health state. More details on the disease model, its parameters, and the dynamic values of effective reproduction number under different scenarios are available in the Supplemental Information.

### Non-pharmaceutical interventions

We apply a number of social distancing strategies to mitigate the spread of COVID-193. We assume there are no vaccines available and non-pharmaceutical interventions (NPI) are the only way to control the spread of COVID-19. We use the following NPI strategies: (i) Voluntary home isolation (VHI)—symptomatic people choose to stay at home (non-home type contacts are disabled) for 14 days. (ii) School closure (SC)—schools and colleges are closed (school type contacts are disabled). (iii) Stay home (SH)—a lockdown order directs people to “stay-home” (non-home type contacts are disabled).

School closure and stay-home interventions start on different days in different states as stated in33,34. Once closed, schools are assumed to remain closed until end of August. The duration and compliance to social distancing measures vary across scenarios as shown in Table 1.

Stay-home durations are set at 0, 30, 45 to 60 days. Compliance to SH and VHI are set at 60%, 70%, 80% and 90%. Table 1 lists all the scenarios including the unmitigated one. For each experimental cell, 25 simulation replicates are run and results are shown based on the average values across these runs. Table 2 shows the parameters used in the experiments for easy reference.

### Medical costs

Medical cost of treating COVID-19 patients under different health states are taken from3,35, which provide the average payment for treating pneumonia cases among “large employer health insurance” plans, and under different severity levels. See Table 3. In the absence of COVID-19 treatment cost data, the pneumonia estimates have been used as a proxy. Note that each infected individual’s medical cost is counted only once. For example if a person is in ventilated state, after having gone through “medAttend” and “Hosp” state, costs are cumulative to the “vent” state3.

To estimate the medical costs of COVID-19 for each scenario, we multiply the number of medically attended, hospitalized, and ventilated with the estimated treatment costs per person given in Table 3. This is repeated for each replicate in the simulation and the average estimates are reported. Note that an earlier paper focuses entirely on the medical costs3 and provides more details on medical costs to the interested reader.

### Economic sectors and their interdependencies

We use the summary level input–output (I–O) tables for 2018 downloaded from the US Bureau of Economic Analysis (BEA)36, which quantify how industries depend on each other and interact with each other, to capture the cascading effect of labor supply shock across industries. The entire economy is divided into 71 industries; the I–O data reflects the structure of the US economy and the relative importance of each industry with respect to all other industries. We follow the NAICS (North American Industry Classification System) codes to aggregate the I–O data to sector level (21 sectors). Figure 3 shows the interdependencies between the 21 sectors. The row sectors of Fig. 3 provide input to the column sectors of the figure.

### Data on telework by sector

During the stay-home order, some individuals are able to work from home. However, the ability to work from home (WFH) and the productivity of WFH workers vary by the type of sector the individuals are employed in. Authors in17,37 estimate the number of jobs that can be done from home in the US. Work in17 combines the feasibility of working from home by occupation, with occupational employment counts, and determines that 37% of all jobs in the US can be done from home.

Although this is not uniform across all sectors and cities; sectors like computing, education, legal and financial can be largely operational from home but construction, farming and hospitality cannot be17, provides the fraction of jobs that can be done from home by NAICS (North American Industry Classification System) and by SOC (Standard Occupational Classification) occupation. We use this fraction for each sector (as shown in Fig. 4) to determine the fraction of labor that can work from home. In addition17, provides the fraction of teleworkable wages for each sector. Together, these fractions determine the level of productivity that can be maintained during a lockdown by the healthy workforce in each sector. The health of each individual is tracked by the disease model given in section 3.2.

### Input–output model

We use the Dynamic Inoperability Input–Output Model (DIIM) stated in16,38 to study the effect of labor supply shock arising from the morbidity and mortality caused by COVID-19, as well as the enforcement of the stay-home order, on national productivity. The DIIM model uses the classic input–output (I–O) economic analysis of Leontief (1935)39 to account for the interdependencies between sectors.

I–O models have proven useful in accounting for the flows of goods and services across producing and consuming sectors of the economy. In the US, the Bureau of Economic Analysis is responsible for publishing I–O tables, gross domestic product, and other economic multipliers that are useful for conducting impact analysis of disasters. Each sector requires inputs from other sectors, and in turn produces outputs that are either used as intermediate inputs by other sectors or finished goods or services to satisfy exogenous final demands. Aside from the intermediate inputs, the so-called “value added” is a category of production inputs that are considered exogenous to the interdependent sectors. Within the “value added” is labor, which is the focus of this paper since it is the factor of production that is rendered “inoperable” by the pandemic. The DIIM quantifies the initial sector inoperability parameters by determining the extent to which labor is impacted in each sector.

Additionally, it allows modeling of resiliency parameters within the I–O model to signify sector wise recovery rates. Of particular relevance to this paper are resilience strategies, such as teleworking, that a sector can implement in order to reduce the impact of labor availability on its production of goods and services. We use the DIIM model to estimate the direct effect of drop in labor supply to each sector due to sickness, deaths and lockdown, as well as the indirect effect to sectors that arise due to interdependencies between sectors.

Depending upon the scenario considered in the simulation, appropriate interventions are applied to the social network. The interventions result in removal of edges on a temporal basis in the social contact network. For example, a stay-home order results in removal of all non-home edges of the compliant individuals for the duration of the order. The COVID-19 disease model is seeded and run on this time-varying social contact network over a period of one year. Everyone in the population is assumed to be susceptible at the beginning of the simulations except the seed nodes or the index cases, which are assumed to be infected. As the disease spreads through the network, the simulation generates a time series of daily infections. The infected individuals are further divided into medically attended, hospitalized, ventilated and dead, based on the probabilities assumed in the disease model.

To calculate the labor supply shock to each sector and its impact on productivity, we estimate (i) the number of infected and dead each day in each sector (using occupation and NAICS codes) and calculate the fraction of labor that is unable to work; (ii) the healthy individuals who comply with the stay-home order and do not go to work, and also cannot work from home given their occupation-type, as determined by telecommuting data for each sector17; and (iii) healthy individuals who can work from home but their productivity is reduced as suggested in the teleworkable wages for each sector in17.

## Results and discussion

We calculate the economic losses under the unmitigated scenario and the mitigation scenarios. Mitigation efforts help control the spread of the disease and hence reduce the total number of infections but they also increase the economic losses due to social distancing measures like the stay-home order. The compliance to NPIs and the length of the NPIs determine the extent of the loss, which can be weighed against the benefits measured in terms of reduced number of infections and deaths.

### Economic losses due to inoperability and NPIs

Figure 5 shows the economic losses due to the inoperability of sectors under different NPIs and the infections caused by the pandemic. The left subfigure does not include the economic burden imposed by the treatment and medical services given to the infected individuals.

Lockdown and other social distancing measures reduce the labor supply to sectors but these measures do not uniformly affect each sector’s output. Depending upon how labor-intensive a sector is, how many jobs can be done from home, and how much value each job generates in a sector, the lockdown has a differential impact on each sector. For example, Education, Professional services, and Management sectors are teleworkable at 80% or higher levels whereas Accommodation (includes hospitality and food services) is at 3% and Agriculture is at 7%.

Inability to work from home in Construction and Agriculture sectors should imply more losses in these sectors. However we find that the losses are higher in Education, Professional services and Management sectors because jobs in these sectors pay more on average than the jobs in Construction and Agriculture sectors. Hence even a 20% loss in work in the former sectors can result in a higher total loss in value compared to a 90% loss in work in the latter sectors.

Overall economic losses from inoperability also depend on the level of dependency each sector has on others. Agriculture and Construction sectors have a higher level of dependency on other sectors compared to Education, Professional and Management sectors as shown in Fig. 3. The lack of self-reliance increases the potential for losses caused by the cascading effect from other sectors.

The results in left Fig. 5 show that as the duration of SH order increases, the economic losses increase for a given compliance rate. This is because a longer SH order implies that healthy individuals are not able to work. A longer SH order also reduces the number of infections and deaths and hence improves labor supply and productivity. There is less absenteeism due to sickness and death, and less cascading effect on other sectors. The overall drop in productivity from a longer SH order shows that the gain in productivity from fewer infections and deaths is less than the loss from a longer shutdown. However SH order saves tens of thousands of lives and millions of infections as described in Section 4.4.

In the unmitigated base case, the economic loss is low but the loss due to morbidity and mortality is high. The healthy individuals are assumed to be working in the unmitigated scenario since no NPIs are in effect. The drop in productivity is caused only by the drop in labor supply due to illness and deaths since there is no lockdown in place. However, in the unmitigated case, more than 117,000 lives are lost and over 116 million infections occur.

## Limitations

This study does not consider the demand side shock to the economy that results in drop in demand for goods and services due to lower employment, lost wages, and uncertain economic conditions. Unlike the general equilibrium model where demand and supply shock result in price adjustment, the input–output model does not capture the price dynamics that arise from changes in demand and supply. The treatment costs are average costs for treating pneumonia patients as available from35 which do not vary by age, but only by severity of the case and these are used as proxies for COVID-19 medical costs.

## Summary and conclusions

This study estimates the epidemiological and economic impact of several counterfactual intervention scenarios to contain the spread of COVID-19. Results show that any intervention involving a stay-home order will result in significant economic losses. However, the epidemiological impact of these interventions is dramatic. We find that interventions scenarios involving 45 days of SH order and a high compliance to NPIs can save more than 110,000 lives and 115 million infections compared to the unmitigated case.

We perform a sector level impact analysis and find that losses depend on the level of labor supply shock, the ability of employees to work from home, the productivity of workers who work from home and the dependency between sectors. The sectors that are more labor intensive such as Agriculture and Construction are not the worst performers because the per capita value generated is lower in these sectors compared to sectors like Government and Health.

Our results also show trade-offs between the economic losses and the number of deaths and infections averted. A longer lockdown and/or a high compliance to NPIs result in higher economic losses but save lives and reduce the number of COVID-19 infections. There is also a trade-off between duration of the lockdown and the rate of compliance to NPIs. If people are non-compliant to NPIs, public health policy-makers can increase the duration of the lockdown to get the same level of results in terms of infections and deaths averted.