Balancing Fiscal and Mortality Impact of SARS-CoV-2 Mitigation Measurements
BBalancing Fiscal and Mortality Impact of SARS-CoV-2Mitigation Measurements
Mayteé Cruz-Aponte a,d, ∗ , José Caraballo-Cueto c,b,d a Department of Mathematics-Physics b Department of Business Administration c Director, Census Information Center d University of Puerto Rico at Cayey, Cayey, PR 00737
Abstract
An epidemic carries human and fiscal costs. In the case of imported pandemics,the first-best solution is to restrict national borders to identify and isolate infectedindividuals. However, when that opportunity is not fully seized and there isno preventative intervention available, second-best options must be chosen. Inthis article we develop a system of differential equations that simulate both thefiscal and human costs associated to different mitigation measurements. Aftersimulating several scenarios, we conclude that herd immunity (or unleashing thepandemic) is the worst policy in terms of both human and fiscal cost. We foundthat the second-best policy would be a strict policy (e.g. physical distancingwith massive testing) established under the first 20 days after the pandemic,that lowers the probability of infection by 80%. In the case of the US, this strictpolicy would save more than 239 thousands lives and almost $170.8 billion totaxpayers when compared to the herd immunity case.
Keywords:
COVID-19, epidemic model, fiscal impact, social distancing,physical distancing
JEL:
I1, H3, H4 ∗ Corresponding author
Email addresses: [email protected] (Mayteé Cruz-Aponte ), [email protected] (José Caraballo-Cueto)
Preprint submitted to Journal of Public Economics June 3, 2020 a r X i v : . [ q - b i o . P E ] J un . Introduction During the COVID-19 pandemic, many policymakers are usually facing twoseparated sources of information: economic models that usually predict aneconomic collapse [15] and epidemic models that focus on death counts [12].However, both the economic and mortality figures are key policy variables duringa pandemic but few articles integrate both approaches [9, 16]. In particular, noresearch (to our knowledge) has analyzed both the fiscal and mortality impactof different mitigation measurements. In this article we strive to fill that gapby approximating the impact of physical distancing and patient care on thedeath toll and government budget, in a attempt to find the optimal conditionsto balance it all.Vaccination or therapeutics can eradicate epidemics from the population, likethe case of smallpox [2, 3] but when a newly discovered virus hits the population,the entire world is at risk because everyone is susceptible as in the case of thenovel SARS-CoV-2 that is impacting us in 2020 [13]. In the case of an importedinfection (i.e. not an endemic epidemic), the first-best strategy would be tocontrol borders, identify, treat and isolate infected individuals. This occurredin the U.S. with the Ebola virus, which never became an epidemic [7]. Butwhen a virus is already circulating in a territory and there is no antidote ormassive testing and contact tracing available, social or physical distancing is analternative to mitigate a pandemic and provide the scientific community timeto research and find alternative measures such as an effective treatment or avaccine. Also, physical distancing measure gives fragile healthcare systems theleverage to take care of chronically ill patients without saturation of existingcapacity. What are the fiscal and human costs of all these measurements in theshort and long run?Thus, two research questions drive this study: What is the optimal physicaldistancing policies in a country and what are the implications of these policiesfor both the government budget and loss-of-life? We constructed an enhancedmathematical SIR (Susceptible, Infected, Recovered) epidemic model [5] to2imulate the COVID-19 epidemic in the US in an attempt to estimate the fiscalimpact and the optimal conditions to mitigate this ongoing pandemic. We foundthat a policy of no physical distancing or a race towards herd immunity is notthe optimal policy choice when both human and fiscal costs are considered.In Section 2 we lay out our methodology. In Section 3 we show the dynamicsassociated to our calibrated system of differential equations. In Section 4 wediscuss our results and in Section 5 we conclude and recommend public policies.
2. Methodology
We first describe a simple economy with three sectors; businesses, government,and a household sector with two actors. In the second part of this section wedescribe our epidemic model.
In this economy, the household sector is mobile within the country and iscomposed of L workers and U individuals that are not working. Thus, employmentis less than full. This characterization allows us to consider the supply shocksassociated to the COVID-19 pandemic [10], where laborers are impeded to workfully because of lock-downs or infections affecting members of the householdsector.Firms produce goods and services i, which require X amount of L. A fixedamount of total output y is predetermined to be produced in period t=0 andis given by, y = (cid:80) X i ∗ L i . However, firms are able to adjust its output whenexternal changes hit the labor stock. The total output that considers the impactof such external changes is observed in, Y t = yH t where H t = dL/dt .We hold the following assumptions over H: • if physical distancing is implemented at t=1, H t = − . during the physicaldistancing. When the physical distancing ends in t=n, and H t = n = 0 . This setting let us capture the V-shape growth that is being projected [11]in the post-COVID-19 period. 3 if no physical distancing is implemented, the pandemic ends in t=n+j, H t = n + j +1 = 0 , and H t
Rate of hospitalization(critical illness) 20% Estimated φ Recovery rate after treated(hospital discharge) 14 days Estimated σ recovery rate (mild casesno hospitalization needed) 14 days Estimated δ Death rate due to illness 3%/365 [17] τ Tax rate 0.24 [4] y GDP 21.73 trillion divided by365 days BEA H t changes in the labor stock .5 during physical distanc-ing, 1.06 afterwards or 0.7if no physical distancing isever implemented) M v Cost of treatment 2,294 average treatment di-vided by average days [14] M p money transferred by thegovernment to low-incomeindividuals 22,265 [18] P Fraction of dead individ-uals who received moneytransfer from the govern-ment 0.8 of victims receivedtransfers. About 80% ofdead individuals are elderand we assume that thereis no disproportion of low-income persons in otherages. [19, 20]
Table 1: Parameters of the Epidemiological and Fiscal dynamic model for COVID-19 and theUSA budget. pandemic. 6he parameter values in our table were taken from a recollection of the eventsdeveloping on COVID-19 and the literature. Perturbations around the meansshowed in Table 1 may affect the quantitative magnitude of our figures, butresults are qualitatively similar after such perturbations. In other words, ourfindings for the second-best scenarios are robust to deviations of our parameters:such deviations will largely scale up or down the quantitative aspects of eachscenario.
The parameters of the model were fitted or estimated to maintain a basicreproductive number relatively close to . . For comparison purposes lets notethat the (cid:60) of seasonal influenza ranges approximately within 1.7 to 2.1 [21].For the 2009 influenza A-H1N1 the (cid:60) was estimated to be between 1.2 to 1.6.In particular, the basic reproductive number (cid:60) is the number of secondarycases a single infectious individual generates during the period of infectivity ona completely susceptible population. We assume that the entire population issusceptible such that S ≈ N and that the epidemic has not started in t=0. Theindividuals that can potentially infect the population in our model are infectedindividuals that are either symptomatic or asymptomatic. Treated individualsare assumed to be quarantined. Following the related literature [22], we use thenext generation operator to compute the (cid:60) . Let the vector F be the rate ofnew infections flowing to the latent compartment and the vector V to be therate of transfer of individuals out of the compartment that are able to transmitthe disease. Then, using our SIR system of equations we define F = β S + µIN and V = αE − qαE + γA − (1 − q ) αE + ( (cid:15) + δ + σ ) I In order to compute (cid:60) , let the gradient of F be defined as F = (cid:2) ∂F∂E , ∂F∂A , ∂F∂I (cid:3) and let the gradient of V be define as V = (cid:2) ∂V∂E , ∂V∂A , ∂V∂I (cid:3) then we get:7 = µβ β and V = α − qα γ − (1 − q ) α (cid:15) + δ + σ ) Then (cid:60) is the spectral radius of the second generation operator ρ ( FV − ) also know as the dominant eigenvalue of the matrix FV − . Hence, FV − = µβ β α qγ γ − qδ + σ + (cid:15) δ + σ + (cid:15) = β [ µq ( δ + σ + (cid:15) ) − γq + γ ] γ ( δ + σ + (cid:15) ) µγ δ + σ + (cid:15) ) Then the dominant eigenvalue of FV − is ρ ( FV − ) = β [ µq ( δ + σ + (cid:15) ) − γq + γ ] γ ( δ + σ + (cid:15) ) , whichmeans that the basic reproductive number is: (cid:60) = β [ µq ( δ + σ + (cid:15) ) − γq + γ ] γ ( δ + σ + (cid:15) ) (9)Our intention in this article is to study the impact of the COVID-19 epidemicin an attempt to estimate the optimal conditions to mitigate the fiscal andmortality impact associated to this pandemic. Thus, the stability of the systemand equilibrium points will not be addressed, only the (cid:60) was computed. Wefocused our efforts on simulating scenarios, which are presented in the next setof sections.
3. Physical distancing dynamics generalization
In order to go through the methodology of our simulations we lay out simple8cenarios where we represent the effect of implementing public health policiessuch as physical distance dynamics within our model. In order to simulate theeffect of reducing the infection rate by lowering the contact rate within thepopulation, we modulate the infection ratio β with a time dependent piece-wisecontinuous function Equation 10, f ( t ) , that lowers the infection rate for time t pdOn where physical distancing policies are implemented and raise the infectionrate after time t pdOff . This late increase of the infection rate is not to its full forcebecause we need to account for the measures taken by the population to preventinfections such as using mask and being more sanitized until a determined time t ∗ that either restarts physical distance measures or is the end of the simulatedperiod. See Appendix A for an example on the physical distancing mechanism. f ( t ) = , ≤ t < t pdOn , No physical distancing [0 . , . , t pdOn ≤ t ≤ t pdOff , Physical distancing [0 . , . , t pdOff < t < t ∗ , Measures relaxed (10)
4. Fiscal and Mortality implications under physical distancing sce-nario: The Case of the US
We simulate the effects of varying infection rates in the total population ofthe US. In the case shown in Figure 1, we assume that distancing policies areimplemented two days after the start of the epidemic. The grey line illustratesthe effect of varying the probability of infection within the population: first theprobability is reduced by 90% for four weeks due to an extreme measure (e.g.because of a lock-down with quick massive testing), then is relaxed to 50% foreight weeks, then two cycles of extreme measurement for four weeks followed bya relaxation of 25% for 8 weeks and onward. This 25% reduction in the originalinfection rate β assumes that people are more careful and take personal decisionsto avoid infections. The black line, on the other hand, represents the case whenno physical distancing measures are ever implemented.9 igure 1: Alternated physical distancing starting two days after the epidemic, as described onTable 2. Fiscal and death figures are affected by the number of individuals thatcirculate in the economy. The top left graph illustrates the symptomatic casesbased on the modulation of the physical distancing measures, as shown in thebottom left graph. Note that in the case of no physical distance or herd immunity,the infections grow faster and earlier than in the modulated case, as shown bythe black line. Because the government has to treat those cases in a fast-trackbasis, the fiscal impact of no physical distance is reflected earlier than in thecase of alternated physical distance. Note that the economies obtained by thegovernment when low-income individuals who receive money transfers die arenot sufficient to offset the fiscal losses associated with the pandemic. Humancosts also come up earlier in the case of no distancing, as shown in the bottomright graph where cumulative dead cases are illustrated in Figure 1.In the long run, herd immunity has a higher death toll and implies moregovernment expenditures than the alternated intensity of physical distancing, asshown in Table 2. In particular, with no physical distancing would die 10,689more individuals than in the alternated scenario and the government would lose$1.16 trillion more than in the varying physical distancing. Note that under the10lternated scenario scientists have approximately 400 days to find an antidotewith a very low number of victims, vis-a-vis 150 days under the no distancingcase.
Figure 2: Varying physical distancing starting two days after the epidemic: lowering theinfection rate 20% for four-week intervals and increasing it between 50% to 75% for eight weeksintervals as described on Table 2.
Reduction in probability of infection CumulativeDeath cases Budget after 800 daysNo measures 239,646 $2,090,225,896,15920% for 4 weeks,50% for 8 weeks 228,956 $3,106,451,634,58520% for 4 weeks,75% for 8 weeks (twice)75% afterwards10% for 4 weeks,50% for 8 weeks 228,957 $3,249,326,371,35510% for 4 weeks,75% for 8 weeks (twice)75% afterwards20% for 8 weeks,50% for 4 weeks 228,946 $2,609,322,982,25920% for 8 weeks,75% for 4 weeks (twice)75% afterwards60% for 800 days 212,539 $464,708,870,04720% for 800 days 0 $2,260,976,930,754
Table 2: Cumulative death cases and fiscal impact of Figure 1, 2, and 3
On Figure 2, we illustrate the simulated figures that are obtained when weshorten the length of the cycles showed previously. Here we are also holding11he assumption that the pandemic started in day two. The variation in theprobability of infection is shown in the gray line, which goes first to an extremereduction of 80% for four weeks, then is relaxed to 50% for eight weeks, thentwo cycles of extreme measurement for four weeks followed by a relaxation of25% for eight weeks and onward. The black line here also illustrates the casewhen no physical distancing measures are ever implemented.Similar to Figure 1, here the black line peaks first while the restriction onpopulation mobility postpones and lowers the infection curve. The final amountsfor cumulative deaths and the budget are presented on Table 2. We observedthat the strict alternated scenario of Figure 1 would save the federal government$142.9 billion more than in the relaxed scenario of Figure 2, while mortalityis virtually the same. In other words, the distancing cycles shown in Table 2appear to be less optimal than in the more restrictive case of Table 2.
Figure 3: Changing week length to the case of Figure 2
What would be the effect of holding the same levels of distancing but changingthe length under each regime? In particular, if we enhance the period underthe restrictive infection and shorten the relaxation in each cycle, how would thedeath toll and the fiscal cost change?In Figure 3 we observe that the peak of infection is postponed further when12ompared to the regime of Figure 2, leaving close to 100 days more for thedevelopment of an antidote. If no antidote is ever found in 500 days, under theseenhanced cycles 10 fewer people would die than in the case of Figure 2 wherethe same probabilities of infection are assumed. However, in the case of the costthat this pandemic represents to the federal budget, this restrictive regime ofFigure 3 costs $497.1 more billion than in the cycles of Figure 2.
Figure 4: Effects of persistent distancing after day two of the pandemic
Reduction in probability of infection CumulativeDeath cases Budget after 800 daysNo measures 239,646 $2,090,225,896,15960% for 800 days 212,539 $464,708,870,04720% for 800 days 0 $2,260,976,930,754
Table 3: Cumulative death cases and fiscal impact of persistent and early distancing of Figure4
If we let the probability of infection to be lessened by 80% of distancingto be in place for the whole period, then virtually no one would die out ofCOVID-19. This persistent measure would save 239,646 lives with respectto what would have occurred without health policies. However, if the samepersistent distancing reduced the probability of infection by 40%, mortality13ould be 27,107 lower than the herd immunity scenario. In the case of the fiscalcosts of the different alternatives, budget is presented in Table 3. Since thereis no infection curve in the restrictive and permanent case, the budget of thegovernment is mostly affected by the decline in tax revenues caused by loweredeconomic output. However, when infection rate is lowered just by 40%, thegovernment budget becomes highly impacted after day 400: once infection startsto increase, the public sector is affected by both spending more in treatmentand by the reduction in tax revenues caused by the economic collapse. In thecase of no physical distancing, even though economic output decreased, thefederal budget is highly reduced by the treatment cost. At the end, if there is anopportunity to implement a persistent and early public health policy, it wouldbe better to do it intensely (e.g. by combining a strong physical distance withmassive testing): otherwise, the relatively human and fiscal cost would increasesignificantly.How would the figures change if the persistent measure is implemented late?The evolution of infection and mortality is similar, but there are differences inthe long run for the associated fiscal costs. When the infection is reduced by40% or 80%, the associated cost of the pandemic to the government decreasedby $51.4 billion than when the public health policy is implemented earlier likein Figure 4. This difference arises because the economy was not halted duringthe first weeks of the pandemic. That is, even in the case of these late decisionsthe government is better off in implementing the strict measure: death toll doesnot change while fiscal costs perform much either in day 2 or day 20 after thepandemic (See Appendix B).In Figure 5 we show the effects of lowering the probability of infection withinthe whole U.S. population for different time intervals. When infection is reducedby 90% for eight weeks, mortality is 10,713 lower than in the herd immunitycase and the fiscal cost of the pandemic is the minimum with respect to any ofthe scenarios presented in this article. That is, this short and strong distancingpolicy would have a lower death toll (24 deaths) than in the alternated scenarioof Figure 1, but with a lowered fiscal cost ($180.3 billion less).14 igure 5: Varying probability of infection between 10% and 50% with different time intervals,two days after the pandemic
Reduction in probability of infection CumulativeDeath cases Budget after 600 daysNo physical distancing 239,646 $2,090,225,900,89610% for 8 weeks 228,933 $3,429,605,751,03850% for 24 weeks 228,941 $2,789,411,480,863
Table 4: Cumulative death cases and fiscal impact of varying probability of infection between10% and 50% with different time intervals of Figure 5
If the infection rate is reduced by 50% for twenty four weeks, the death tollis a bit higher than in the case of a strong policy for eight continuous weeks. Ineither case, the pandemic would kill at least 10,705 fewer individuals than inthe herd immunity case. In terms, of budget, the longer period under distancinginduces a larger fiscal decline than in the case of the eight-week distancing.However, the herd immunity is again the most costly option in terms of bothdeath and government budget.These results reveal that if a policymaker is going to implement distancingmeasures, overall better results would be found with a strict measure for a shortperiod than with a weak measure for a long period. In fact, in terms of humanand fiscal costs, we can state that this strong policy for eight continuous weeks15s the preferred option after the case of Figure 6.
Figure 6: Effects of persistent distancing implemented in day 20 of the pandemic.
Reduction in probability of infection CumulativeDeath cases Budget after 800 daysNo measures 239,646 $2,090,225,896,15960% 212,539 $516,145,614,62420% 0 $2,312,415,608,494
Table 5: Cumulative death cases and fiscal impact of persistent but late distancing on Figure 6
5. Conclusions and Policy Recommendations
A challenge that policymakers face during a pandemic is to save lives atthe minimum fiscal costs. In the case of COVID-19, the first-best policy tominimize human and fiscal costs would be reached by identifying, treating,and isolating incoming infected individuals. When this opportunity is missed,second-best policies need to be searched. We conclude that, when both fiscaland human costs are equally relevant, the second-best policy is reached whenpolicies to significantly reduce the transmission rate are taken. In particular,if the transmission rate is lowered by 80%, either in day 2 or day 20 after the16eginning of the pandemic (see Appendix B) , both human and fiscal costsassociated to the pandemic are minimized with almost no dead cases and $2.57trillion in net impact to the government budget. These early policies can takethe form of physical distancing combined with massive testing.The third best policy is found when a strong lock-down or similar policyreduced the infection rate by 90% for eight weeks. If one focuses only on moneydisregarding life, this policy is the second-best policy: the pandemic wouldcost approximately $1.4 trillion. The fourth best policy is to alternate physicaldistancing measures: strict distancing for four weeks followed by a mild relaxationof eight weeks, then two cycles of returning to strict distancing for four weeksfollowed by eight weeks of relaxation.Unleashing the pandemic without taking any containment policy does notminimized the fiscal cost of the pandemic in any of our several simulations,except for the case when the transmission rate is reduced mildly. But even whencompared to that case of a permanent reduction of 40% to the infection rate,this herd immunity case still results in 27,107 more lives lost. This is becausethe race towards herd immunity always had the greatest human costs. In fact,at the time of our writing, scientists cannot clearly state that immunity is foundafter surviving the infection [8, 6].We do not consider what type of fiscal policy can be implemented to counteractthe fiscal costs associated to the pandemic. Instead, we attempt to identify thecost of the pandemic and, from that amount, fiscal policies can be tailor-madeto address specific needs.We acknowledge that our model may not be exported to developing countrieswhere the lock-down can also result in deaths of individuals from starvation:given the low safety nets and salaries in many poor countries, lack of employmentcan severely reduce dietary intake resulting in other serious health-related issuesor death. In that case, we recommend adding a death variable associated toforced unemployment. Such an approach exceeds the scope of this paper.17 . Acknowledgments
We like to thanks Dr. Ricardo González-Méndez from the University ofPuerto Rico School of Medicine as well as Dr. Ricardo J. Cordero-Soto fromCalifornia Baptist University for their insights and suggestions. The usualdisclaimers apply.
7. Disclosure • Both authors contributed equally in the designed, codification and prepa-ration of the article. All authors have approved the final article. • This research did not receive any specific grant from funding agencies inthe public, commercial, or not-for-profit sectors. • Declarations of interest: none
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Appendix A. Physical Distance Mechanism
Let’s look at Figure A.7 to explain the mechanism of the physical distancemodulation. In this graph we vary the time length and the ratio of the infectionto simulate the effect of alternating physical distancing measures. The toppanel on Figure A.7 is the dynamic of the symptomatic cases I , where the blackplot represents the scenario where no measures are applied hence there is nophysical distancing f ( t ) = 1 for all t to account for % contact rate, the graygraph is the one applying physical distancing as shown in the bottom graph thatrepresents our piece-wise function f ( t ) .In this example we start physical distancing measures on day 20 (i.e. t pdOn =20 after the start of the epidemic) and lower the transmission rate 50% for twoweeks (i.e. t pdOff = 34 two weeks after implemented + t pdOn = 20 ). Then,measures are relaxed for two weeks. At this time the infection rate is decreasedby 10%, assuming people are a little bit more careful by washing their hands orusing cloth masks. After these two weeks, when cases start to increase again,the physical distancing measures are taken more strictly, thereby decreasing theinfection rate by 70% for six weeks. Thus, we found the famous "flatten the curve"scenario in which we all desire to maintain our health system unsaturated. If a21 igure A.7: The effect of alternate physical distancing measures on the epidemic curve. vaccine or effective treatment is not implemented before the physical measuresare lifted, the epidemic will raise again. Appendix B. Other Physical Distance Scenarios
A policymaker would like to find an easier mechanism than a cyclical regime tocombat the pandemic. In Figure B.8 we show the case where just one restrictivepolicy that declines the infection rate by 80% is applied for 250 days. Theprobability of infection is then kept by a permanent reduction of 25% to accountfor people being more careful and taking measures to avoid being infected. Inthis case the peak of the distancing curve arrives much later than before atapproximately day 600. As expected, more lives (26 persons) are saved than inthe alternated cycles of Figure 2 but now the federal budget is almost halved.Note that in any of these scenarios, no physical distance or herd immunity is anoptimal solution, either in terms of human or fiscal cost.22 igure B.8: Distancing of 20% for 250 days after the pandemic, followed by 75% distancing.
Reduction in probability of infection CumulativeDeath cases Budget after 800 daysNo measures 239,646 $2,090,225,896,15920% for 250 days then 75% 228,930 $2,460,890,014,613