Andrew Atkeson, What Will Be the Economic Impact of COVID-19 in the US? Rough Estimates of Disease Scenarios (2020)

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NBER Working Paper No. 26867 by Andrew Atkeson, What Will Be the Economic Impact of COVID-19 in the US? Rough Estimates of Disease Scenarios, dated March 2020. The note introduces economists to a simple SIR model of the progression of COVID-19 in the United States over the next 12-18 months, dividing the population into susceptible, actively infected and recovered (or dead) categories. It uses the model to make quantitative statements about the tradeoff between the severity and timing of suppression through social distancing and the progression of the disease. Special attention is given to whether and when active infections exceed 1% of the population, at which point the health system is forecast to be severely challenged, and 10%, as well as the cumulative burden over an 18 month horizon.

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NBER WORKING PAPER SERIES

WHAT WILL BE THE ECONOMIC IMPACT OF COVID-19 IN THE US? ROUGH
ESTIMATES OF DISEASE SCENARIOS

Andrew Atkeson

Working Paper 26867
http://www.nber.org/papers/w26867

NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
March 2020

All errors are mine. The views expressed here are entirely my own and not official statements of
the Federal Reserve Bank of Minneapolis, the Federal Reserve, or the National Bureau of
Economic Research.

NBER working papers are circulated for discussion and comment purposes. They have not been
peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies
official NBER publications.

© 2020 by Andrew Atkeson. All rights reserved. Short sections of text, not to exceed two
paragraphs, may be quoted without explicit permission provided that full credit, including ©
notice, is given to the source.
What Will Be the Economic Impact of COVID-19 in the US? Rough Estimates of Disease
Scenarios
Andrew Atkeson
NBER Working Paper No. 26867
March 2020
JEL No. C0,E0

ABSTRACT

This note is intended to introduce economists to a simple SIR model of the progression of
COVID-19 in the United States over the next 12-18 months. An SIR model is a Markov model of
the spread of an epidemic in a population in which the total population is divided into categories
of being susceptible to the disease (S), actively infected with the disease (I), and recovered (or
dead) and no longer contagious (R). How an epidemic plays out over time is determined by the
transition rates between these three states. This model allows for quantitative statements
regarding the tradeoff between the severity and timing of suppression of the disease through
social distancing and the progression of the disease in the population. Example applications of the
model are provided. Special attention is given to the question of if and when the fraction of active
infections in the population exceeds 1% (at which point the health system is forecast to be
severely challenged) and 10% (which may result in severe staffing shortages for key financial and
economic infrastructure) as well as the cumulative burden of the disease over an 18 month
horizon.

Andrew Atkeson
Bunche Hall 9381
Department of Economics
UCLA
Box 951477
Los Angeles, CA 90095-1477
and NBER
andy@atkeson.net
1 Introduction

In the face of the rapidly growing COVID-19 pandemic, a wide variety of SIR models
of the progression of this epidemic are being used by public health experts to generate
scenarios that are being used to guide decisions to recommend and impose increas-
ingly severe mitigation measures on economies worldwide.1 Economists are not fully
familiar with the quantitative implications of these models and thus are not fully
engaged in the policy discussion regarding the tradeoff between the public health
and economic implications of these mitigation and social distancing measures.2

This note is intended to introduce economists to a simple SIR model of the progres-
sion of COVID-19 in the United States over the next 12-18 months. An SIR model
is a Markov model of the spread of an epidemic in a population in which the total
population is divided into categories of being susceptible to the disease (S), actively
infected with the disease (I), and recovered (or dead) and no longer contagious (R).3
How an epidemic plays out over time is determined by the transition rates between
these three states. These transition rates are determined by characteristics of the
underlying disease and by the extent of mitigation and social distancing measures
imposed. This model allows for quantitative statements regarding the tradeoff be-
tween the severity and timing of suppression of the disease through social distancing
and the progression of the disease in the population. The particular model studied is
from Wang et al. (2020).4 Example applications of the model are provided. Special
attention is given to the question of if and when the fraction of active infections in the

1
See Ferguson et al. (2020) for a most recent model-based discussion of the public health
implications of alternative social distancing and mitigation measures. The scenarios outlined in
this paper are sobering. https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/
gida-fellowships/Imperial-College-COVID19-NPI-modelling-16-03-2020.pdf
2
Several early analyses of the economic impact of COVID-19 are coming out. Gourinchas (2020)
and McKibbin and Roshen (2020) are useful discussions of the tradeoff between public health and
economic impact. Barro et al. (2020) uses data from the 1918-19 Spanish Flu epidemic to put
bounds on the impacts of COVID-19 on mortality and economic output.
3
Here I consider a model in which agents cannot get the disease again once they have transitioned
into the R state. It is not yet clear whether this assumption is correct for COVID-19.
4
https://doi.org/10.1038/s41421-020-0148-0

1
population exceeds 1% (at which point the health system is forecast to be severely
challenged) and 10% (which may result in severe staffing shortages for key financial
and economic infrastructure) as well as the cumulative burden of the disease over an
18 month horizon.5

Anderson et al. (2020) published online in The Lancet discusses the issues consid-
ered in this note.6 The figure 1, taken from that paper illustrates qualitatively the
impact of mitigation measures on the cumulative and peak incidence of the disease
over a time horizon of 12 months together with the concern that relaxation of social
distancing measures too early would lead to a resurgence of the disease. The aim of
this note is to introduce economists to the quantitative implications of such models
for alternative mitigation efforts.

5
The scenarios considered here should not be considered definitive forecasts. They are intended
only to allow the reader to see how a model of the progression of the epidemic might be applied to
economic analysis of COVID-19 and to allow readers trained in economics to begin conversations
with public health experts in this area.
6
https://doi.org/10.1016/S0140-6736(20)30567-5

2
gatherings. This
ll provide valuable
Timing and width of peak uncertain due to:
sures. The greater • Stochasticity in early dynamics
• Heterogeneities in contact patterns
ger and flatter the • Spatial variation

Cases being reported
f resurgence when • Uncertainty in key epidemiological parameters

mitigate economic
Social distancing flattens curve
at determine the Risk of resurgence
are what propor- following lifting of
interventions
d symptoms and Epidemic growth,
doubling time
olate and to what 4–7 days

ic individuals take 0 1 2 3 4 5 6 7 8 9 10 11 12

of symptoms; and Months since transmission established

infectious period Figure: Illustrative simulations of a transmission model of COVID-19
A baseline simulation with case isolation only (red); a simulation with social distancing in place throughout the
nked issue of how epidemic, flattening the curve (green), and a simulation with more effective social distancing in place for a limited
hase. period only, typically followed by a resurgent epidemic when social distancing is halted (blue). These are not
quantitative predictions but robust qualitative illustrations for a range of model choices.
control the spread
overnment action, Figure 1: taken from Anderson et al. (2020) in The Lancet
e most important transmission—if this turns out to be a feature of
al advice remotely COVID-19 infection—will determine the success of this
Main Conclusions:
cial distancing are strategy.16
ss gatherings are The Contact
main tracing
messageisfor of economists
high importance derived infrom the simulations
early of this simple SIR
ities and remotely model
stages of to
the contain
evolution ofspread, and
COVID-19 model-based
in the United estimates
States (and likely worldwide) is
with specialised that it
suggest,
will with
likely an R0 value
require severe ofsocial
2·5, that about 70%
distancing measures of maintained for an entire
se. Isolating towns year or
contacts evenwill 18have
months to be successfully
(until a vaccinetracedcan beto control
developed) to avoid severe public
overnment action health
early spread.
consequences.17
Analysis of individual contact patterns
n the early stages suggests that contact tracing can be a successful strategy
Even putting aside concerns about public health, it appears that there is a signif-
any uncertainties, in the early stages of an outbreak, but that the logistics
icant economic tradeoff whether or not we impose social distancing — the economic
entitled contain, of timely tracing on average 36 contacts per case will be
costs of strong social distancing measures imposed for an entire 12-18 months on
K has just moved challenging.17 Super-spreading events are inevitable, and
the one hand or the economic costs of a large cumulative burden of lost work time
atten the epidemic could overwhelm the contact tracing system, leading to
ty. If measures are the need for broader-scale social distancing interventions.
severe economic Data from China, South Korea, Italy, and 3 Iran suggest
ur in the autumn that the CFR increases sharply with age and is higher in
d Iran are at the people with COVID-19 and underlying comorbidities.18
e best care possible Targeted social distancing for these groups could be the
with COVID-19. most effective way to reduce morbidity and concomitant
istics of COVID-19 mortality. During the outbreak of Ebola virus disease
g the time from in west Africa in 2014–16, deaths from other causes
(and life) due to the disease. Which option would have the more severe economic
consequences is hard to determine.

Even under severe social distancing scenarios, it is likely that the health system
will be overwhelmed, which is indicated to happen when the portion of the U.S.
population actively infected and suffering from the disease reaches 1% (about 3.3
million current cases).7 More severe mitigation efforts do push the date at which
this happens back from 6 months from now to 12 months from now or more, perhaps
allowing time to invest heavily in the resources needed to care for the sick. It is clear
that to avoid a health care catastrophe as is currently being experienced in Italy,
prolonged severe social distancing measures will need to be combined with a massive
investment in health care capacity.

Under almost all of the scenarios considered, at the peak of the disease progression,
between 10% and 20% of the population (33 - 66 million people) suffers from an
active infection at the same time. This level of infection in the population will likely
require a significant diversion of the workforce from work to either self quarantine
and recuperation or caring for these sick individuals for a period of weeks or more.
It is likely that all of this would have to occur without adequate support from the
health care system for those with dire cases of the disease even if we implement a
large investment in healthcare. In the model simulations, this peak infection period
occurs between 7-14 months from now. It is imperative to try to understand how
critical healthcare, economic, and financial infrastructure would function in a period
of such concentrated disease burden should this come to pass.

Many are making note of and taking heart from the apparent success of disease mit-
igation efforts in China, South Korea, Taiwan, Hong Kong, and Singapore.8 These
7
See “What does the coronavirus mean for the U.S. health care system? Some
simple math offers alarming answers” available here https://www.statnews.com/2020/03/10/
simple-math-alarming-answers-covid-19/. See also this recent assessment from the European Cen-
tre for Disease Prevention and Control https://www.ecdc.europa.eu/sites/default/files/documents/
RRA-sixth-update-Outbreak-of-novel-coronavirus-disease-2019-COVID-19.pdf
8
see for example https://www.nytimes.com/2020/03/13/opinion/coronavirus-best-response.
html. Wang et al. (2020) study the impact of mitigation efforts in Wuhan on the transmission
of the epidemic. Hellewell et al. (2020) discuss the possibilities for containing the epidemic through

4
areas have experienced remarkable success in reducing the number of new cases and
slowing the growth of the cumulative number of cases from an exponential to a lin-
ear path through a variety of mitigation measures. But is it safe for these countries
to begin to relax their mitigation efforts in the near future so as to resume eco-
nomic activity? Or, as discussed in Anderson et al. (2020), would the disease simply
re-emerge?

To answer this question, I use the model to ask what happens if extremely severe
mitigation efforts are imposed on a temporary basis (for a few months) and then
gradually relaxed. The model predicts that once mitigation efforts are relaxed, the
disease simply restarts its rapid progression and sweeps through the population in
less than 18 months, reaching its peak infection rate about 450 days from now. Thus,
while the mitigation success of these countries is good news, a much more sustained
mitigation effort will be required to capitalize on this success.

In the remainder of this note, I present the model and simulation results.

2 The Model:

The model presented in this note is based on the model presented in Wang et al.
(2020).9 A similar model applied to the Seattle area, presented in Klein et al. (2020)10
was used in advising Seattle area public health officials on the public health measures
undertaken there. Academic models presented to the CDC in February but not made
public were discussed in the New York Times on March 1311 . Various interactive
web-based versions of these models are available online.12 This video provides an
accessible introduction to the mathematics involved.13
isolation and contact tracing https://doi.org/10.1016/S2214-109X(20)30074-7
9
available here https://www.nature.com/articles/s41421-020-0148-0
10
available here https://institutefordiseasemodeling.github.io/COVID-public/
11
see this article https://www.nytimes.com/2020/03/13/us/coronavirus-deaths-estimate.html
12
See, for example https://neherlab.org/covid19/ and https://www.nytimes.com/interactive/
2020/03/13/opinion/coronavirus-trump-response.html
13
https://www.youtube.com/watch?v=Kas0tIxDvrg

5
The model is as follows.

The population is set to N which here we normalize to one, so all results should
be interpreted in fractions of the relevant population.

At each moment of time, the population is divided into four categories that sum
to the total (of one). These are susceptible (no immunity) S, exposed E , infected
I, and recovered (or dead) R. These fractions of the population evolve over time as
follows
S
dS/dt = −βt I
N
S
dE/dt = βt I − σE
N
dI/dt = σE − γI

dR/dt = γI

βt = Rt γ

Following Wang et al. (2020), the parameter γ governing the rate (per day) at
which infected people either recover or die is considered a fixed parameter of the
disease and is set to γ = 1/18 reflecting an estimated duration of illness of 18 days.
Likewise, the parameter σ governing the rate at which those exposed to the disease
become infected is also considered a fixed parameter of the disease and is set to
σ = 1/5.2 reflected an estimated incubation period of the disease of 5.2 days.

The parameter βt is the rate at which individuals who are infected bump into
other people and “shed” virus onto those people. Of the people that they bump into,
fraction S/N are susceptible and hence transition to being exposed. The parameter
Rt is the ratio of this meeting rate βt and the recovery + death rate γ on day t.
This parameter governing the ratio of the rates at which those susceptible become
infected and those ill either recover or die varies over time and is controlled by social
distancing and quarantine measures. We will experiment with various time paths for
this rate Rt .

6
We parameterize this rate Rt to allow for an initial period of intense application
of social distancing measures followed by a relaxation of these measures to allow
economic activity to resume. We do so with the following parameters

R1t = R1,0 exp(−η1 t) + (1 − exp(−η1 t)R̄1

R2t = R2,0 exp(−η2 t) + (1 − exp(−η2 t)R̄2

Rt = (R1t + R2t )/2

Here R0 = (R1,0 + R2,0 )/2 is the initial value of Rt representing the spread of the
disease in its initial phase.

The parameters R̄i for i = 1, 2 indicate the long run values to which Rit converge.
Thus, in the long run Rt converges to (R̄1 + R̄2 )/2. To get a U-shaped pattern for
Rt , we make R1t a rapidly declining function and R2t a slowly rising function The
parameter η1 governs the rate at which R1t falls towards R̄1 . The parameter η2
governs the rate at which R2t rises towards R̄2 .

This parameterization of Rt adds three differential equations to our model

dR1t /dt = −η1 (R1t − R̄1 )

dR2t /dt = −η2 (R2t − R̄2 )
1 1
dRt /dt = − η1 (R1t − R̄1 ) − η2 (R2t − R̄2 )
2 2
with initial conditions Ri,0 .

2.1 Model Parameters:

The parameters γ and σ are set following Wang et al. (2020) as discussed above.

The initial conditions for all experiments are set as follows. The initial value of

7
I is set to one in ten million, corresponding to 33 initial cases in the United States
given a population of 330 million. The initial value of E = 4I, corresponding to
an initial 132 individuals carrying the virus but not yet contagious. These values
roughly correspond to early February of 2020 for the United States. There is a lot
of uncertainty regarding the number of initial cases.

The value of R0 corresponds to the transmission of the disease with no mitigation
efforts. This is a critical parameter for evaluation the progression of the disease in
the population and the economic costs of mitigation. Wang et al. (2020) consider a
value of R0 = 3.1. Remuzzi and Remuzzi (2020)14 estimate value of R0 between 2.76
and 3.25 using data from the outbreak of the disease in Italy. This website reports
an R0 in China of 2.5.15 The model referenced in Appendix 3 of Anderson et al.
(2020) is also R0 = 2.5. The model in this article in the New York Times considers
a value of R0 = 2.3.16 Zhang et al. (2020)17 estimates a value of R0 = 2.28 using
data from the Princess Cruise ship. Fauci et al. (2020)18 report an R0 of 2.2. The
European Centre for Disease Control19 reports R0 as ranging from 2-3.

2.1.1 The impact of mitigation on transmission:

Social distancing and other mitigation steps can reduce the transmission rate Rt .
Wang et al. (2020) estimate a gradual reduction of Rt in Wuhan from 3.1, to 2.6
then to 1.9, and finally to somewhere between 0.9 and 0.5 with increasingly se-
vere mitigation efforts. Kucharski et al. (2020)20 estimate that travel restrictions
in Wuhan imposed on January 23rd reduced Rt from 2.35 to close to 1 one week
later. Li et al. (2020) estimate that mitigation efforts in Wuhan reduced Rt from an

14
https://doi.org/10.1016/S0140-6736(20)30627-9
15
https://www.isglobal.org/en/coronavirus-lecciones-y-recomendaciones
16
https://www.nytimes.com/interactive/2020/03/13/opinion/coronavirus-trump-response.html
17
https://www.ncbi.nlm.nih.gov/pubmed/32097725
18
https://www.nejm.org/doi/full/10.1056/NEJMe2002387
19
https://www.ecdc.europa.eu/sites/default/files/documents/RRA-sixth-update-Outbreak-of-novel-coronavirus-dise
pdf
20
https://doi.org/10.1016/S1473-3099(20)30144-4

8
initial value of 2.38 to an average of 1.36 during the period January 24 to February
3 and an average of 0.99 during the period January 24 to February 8. I take these
types of estimates as a guideline in parameterizing a scenario with temporary but
severe mitigation measures imposed. I consider a reduction in transmission from
3.0 to 1.6 as more in line with milder social distancing measures.21 Anderson et al.
(2020) discuss the uncertainties surrounding estimating the effect of mitigation. It
is critical to revisit the effectiveness of mitigation efforts in slowing the transmission
of the disease as more information comes in from current efforts underway.

I describe the mitigation scenarios I consider below.

3 Model Experiment 1: Constant Mitigation over
18 months

In my first computational experiment with the model, I ask what happens over the
next 18 months holding fixed disease characteristics and mitigation efforts for the
entire time period? To answer this question, I simulate the model under various fixed
assumptions regarding the parameter Rt = R0 governing the effectiveness of social
distancing efforts of increasing severity in slowing the spread of the disease.22

I consider constant values of Rt = R0 of 1.6, 1.8, 2.0, 2.2, 2.5, 2.8 and 3.0. repre-
senting different levels of disease transmission under different mitigation scenarios.23
Note that if the true R0 for COVID-19 in the US is 3, then Rt = 1.6 represents some-
thing close to a 50% reduction of the transmission rate through mitigation measures.

I plot the results for the cumulative cases as a fraction of the population over the
21
This website https://neherlab.org/covid19/ considers “weak” mitigation as capable of reducing
Rt to 80% of R0 , “moderate” mitigation as reducing Rt to 60% of R0 , and “strong mitigation” as
reducing Rt to 40-45% of R0 .
22
To solve the system of differential equations, I use Matlab’s ode113 solver and I set the the
options to opts = odeset(’Reltol’,1e-13,’AbsTol’,1e-14,’Stats’,’on’)
23
To produce a constant value of Rt in the model, I set R̄1 = R̄2 = R1,0 = R2,0 = R0 . The
values of η1 and η2 are arbitrary in this case and can be set to 1.

9
course of 18 months under each scenario for the transmission rate Rt = R0 in Figure
2. Note that under almost all scenarios considered, more than 2/3 of the population
contracts the disease over the course of 18 months, but it takes 200 days for the
cumulative number of cases to build to a crescendo, ripping through the population
between 150 and 400 days from now, suggesting a substantial delay in the full impact
of this disease. It is only in the case that Rt = 1.6 that the disease is contained to
a small fraction of the population over the time period until which time a vaccine
might become available.

1
Rt = 3.0
Rt = 2.8
0.9 Rt = 2.5
Rt = 2.2
Rt = 2.0
0.8 Rt = 1.8
Rt = 1.6

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0
0 100 200 300 400 500 600
days

Figure 2: Cumulative Cases as a fraction of the population over 18 months under different values
of Rt = R0 held constant over the entire 18 month time period

10
I plot the results for the fraction of the population with an active infection over the
course of 18 months under each scenario for the transmission rate Rt = R0 in Figure
3. As discussed above, a rough estimate is that the health system is overwhelmed
when this fraction exceeds 1%. The peak incidence in each case is substantially
above this threshold. It appears to take 150-200 days to reach this threshold, with
peak incidence coming in 250-475 days. It is clear that reductions in Rt through
mitigation efforts do “flatten the curve”, but perhaps not by as much as might be
hoped unless Rt can be held to 1.6 or below for the entire 18 month time period.

0.25
Rt = 3.0
Rt = 2.8
Rt = 2.5
Rt = 2.2
0.2 Rt = 2.0
Rt = 1.8
Rt = 1.6

0.15

0.1

0.05

-0.05
0 100 200 300 400 500 600
days

Figure 3: Fraction of the population with an active infection over 18 months under different values
of Rt = R0 held constant over the entire 18 month time period

11
Finally, I examine the extent to which early information about the epidemic is
helpful in distinguishing which scenario is most likely. To do so, I zoom in on the
number of cumulative cases recorded in the early states of the epidemic over the first
two months or so in figure 4. It appears that it might be difficult to distinguish which
of these scenarios is the relevant one given the uncertainties in actually measuring
the extent of the epidemic in its early phases.24 25

24
Note that the doubling time for the different values of Rt implied by the early phase of this
experiment are 4.9, 5.9, 5.7, 7.3, 8,6, 9.3, and 12.0 days respectively going from the largest to
smallest value of R0 considered.
25
See Li et al. (2020) for a discussion of the extent of unmeasured cases of coronavirus. https:
//science.sciencemag.org/content/early/2020/03/13/science.abb3221.full

12
12000
Rt = 3.0
Rt = 2.8
Rt = 2.5
Rt = 2.2
10000 Rt = 2.0
Rt = 1.8
Rt = 1.6

8000

6000

4000

2000

0
0 10 20 30 40 50 60 70 80
days

Figure 4: Cumulative Cases as a fraction of the population over 2+ months under different values
of Rt = R0 held constant over the entire time period

4 Model Experiment 2: Speed of Mitigation

In this second model experiment, I consider the impact of changing the speed of
mitigation. In all the scenarios considered, I set R0 = 3.0 and set R∞ = 1.6. I
consider alternative speeds with which Rt falls from this initial value to this long-run

13
value (under permanently maintained mitigation measures).26

In Figure 5, I plot the various speeds with which reductions in Rt are implemented
over an 18 month period. In Figures 6 and 7 I plot the corresponding paths for
cumulative cases and actively infected as a fraction of the population over the 18
months. The results of this simulation show remarkably small benefits to speedy
application of mitigation measures in terms of reducing the peak fraction of the
population infected. The primary benefit of speedy mitigation appears to be in
delaying that period of peak infection. Further examination of this point is required.

26
To implement this experiment, I set R̄1 = R̄2 = 1.6 and η1 = η2 equal to values of
1/5, 1/10, 1/20, 1/50, 1/100 corresponding to very fast, fast, moderate, slow, and very slow sce-
narios repectively.

14
3
very fast
fast
moderate
slow
very slow

2.5

1.5
0 100 200 300 400 500 600
days

Figure 5: Reduction in Rt through mitigation imposed at various speeds

15
0.7
very fast
fast
moderate
0.6 slow
very slow

0.5

0.4

0.3

0.2

0.1

0
0 100 200 300 400 500 600
days

Figure 6: Cumulative cases as a fraction of the population under mitigation imposed at various
speeds

16
0.08
very fast
fast
moderate
0.07
slow
very slow

0.06

0.05

0.04

0.03

0.02

0.01

0
0 100 200 300 400 500 600
days

Figure 7: Active infections as a fraction of the population under mitigation imposed at various
speeds

5 Model Experiment 3: Temporary imposition of
extremely severe mitigation measures

In this third model experiment, I consider a path for mitigation efforts that results
initially in a very sharp reduction in Rt and then a gradual relaxation of these
mitigation of these efforts.

The path of Rt considered is shown in Figure 8. Note that here I assume that

17
these efforts result in values of Rt well below 1 for a few months, which results in a
shrinkage of the epidemic during those months.27

2.5

1.5

0.5

0
0 100 200 300 400 500 600
days

Figure 8: Path forRt under temporary extreme mitigation efforts

In Figures 9 and 10, I show the evolution of the cumulative cases of this epidemic
and the number of people actively infected in the first several months under this
temporary severe mitigation. As shown in these figures, the path for Rt assumed does
result in a “bending of the curve” from exponential to less than linear growth and a
27
The parameter values that generate this path are R1,0 = 10, R2,0 = −4, R̄1 = −4, R̄2 = 10,
and η1 = 1/35, η2 = 1/100

18
substantial reduction in the number of people actively infected just as seen recently in
China, South Korea, Taiwan, Singapore, and Hong Kong. Is this temporary success
grounds for optimism?

2500

2000

1500

1000

500

0
0 20 40 60 80 100 120 140 160
days

Figure 9: Cumulative cases as a fraction of the population under temporary severe mitigation
efforts

19
500

450

400

350

300

250

200

150

100

0
0 20 40 60 80 100 120 140 160
days

Figure 10: Number of people actively infected under temporary severe mitigation efforts

In figures 11 and 12, I show the path for cumulative cases and those actively
infected as a fraction of the total population over the full 18 month period that
includes relaxation of the severe mitigation. As is clear from the figures, the epidemic
comes roaring back early in its second year if mitigation is relaxed.

20
1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0
0 100 200 300 400 500 600
days

Figure 11: Cumulative cases as a fraction of the population under under temporary severe miti-
gation efforts

21
0.25

0.2

0.15

0.1

0.05

0
0 100 200 300 400 500 600
days

Figure 12: Active infections as a fraction of the population undertemporary severe mitigation
efforts

6 Conclusion

The simulations of the model in this note, and, even more so, the fully detailed
analysis in Ferguson et al. (2020), paint a grim picture of the choices regarding public
health that policymakers face in mitigating the impact of the COVID-19 pandemic.
What is urgently needed is an economic analysis of the economic consequences of
the mitigation steps currently being implemented and contemplated going forward
so that economic tradeoffs between public health and the economy can be considered

22
quantitatively. I hope that academic and policy economists find this model useful in
carrying out that analysis.

23
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