Impacts of export restrictions on the global personal protective equipment trade network during COVID-19
Yang Ye, Qingpeng Zhang, Zhidong Cao, Frank Youhua Chen, Houmin Yan, H. Eugene Stanley, Daniel Dajun Zeng
aa r X i v : . [ phy s i c s . s o c - ph ] J a n Impacts of export restrictions on the global personal protective equipment tradenetwork during COVID-19
Yang Ye, Qingpeng Zhang, ∗ Zhidong Cao,
2, 3, 4
Frank YouhuaChen, Houmin Yan, H. Eugene Stanley, and Daniel Dajun Zeng
2, 3, 4 School of Data Science, City University of Hong Kong, Hong Kong SAR, China The State Key Laboratory of Management and Control for Complex Systems,Institute of Automation, Chinese Academy of Sciences, Beijing, China School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing, China Shenzhen Artificial Intelligence and Data Science Institute (Longhua), Shenzhen, China Department of Management Sciences, College of Business,City University of Hong Kong, Hong Kong SAR, China Department of Physics, Boston University, Boston, MA 02215, USA
The COVID-19 pandemic has caused a dramatic surge in demand for personal protective equip-ment (PPE) worldwide. Many countries have imposed export restrictions on PPE to ensure thesufficient domestic supply. The surging demand and export restrictions cause shortage contagionson the global PPE trade network. Here, we develop an integrated network model, which integratesa metapopulation model and a threshold model, to investigate the shortage contagion patterns. Themetapopulation model captures disease contagion across countries. The threshold model capturesthe shortage contagion on the global PPE trade network. Results show that, the shortage conta-gion patterns are mainly decided by top exporters. Export restrictions exacerbate the shortages ofPPE and cause the shortage contagion to transmit even faster than the disease contagion. Besides,export restrictions lead to ineffective and inefficient allocation of PPE around the world, which hasno benefits for the world to fight against the pandemic.
The COVID-19 pandemic is spreading rapidly aroundthe world. As of Jan 24, 2021, it has infected more than96 million people and claimed more than 2 million livesworldwide [1, 2]. Many countries have adopted a series ofpublic health measures to contain the epidemic, such asthe closure of commercial activities, bans on travel, andexport restrictions [3–5]. Personal protective equipment(PPE), such as face and eye protection devices, protec-tive garments, and gloves, is the most heavily affectedcategory of commodities in export restrictions. Over 73governments have imposed export restrictions on PPEexports [6, 7]. Since the COVID-19 pandemic has causeda growing demand for PPE worldwide [8–10], countriesimpose export restrictions to prepare for the potentialdomestic demand.Recently, several empirical studies have discussed thepros and cons of export restrictions on medical supplies,foods, drugs, etc., in the time of COVID-19. They con-cluded that export restrictions might cause uncertainty insupply and other negative security consequences, thoughthese restrictions seem logical and justifiable [5, 7, 11].Demand surges and export restrictions cause shortagecontagion on the trade network. There is rich economicliterature using quantitative models to investigate thecontagion patterns and their impacts on internationaltrade [12–16]. In physics, a wide range of research pro-posed different models to analyze the dynamics of conta-gion propagation on interdependent networks [17], for ex-ample, the diffusion model [18] and the threshold model[19, 20]. However, how the shortage contagion trans-mits on the global PPE trade network during large-scale epidemic like the ongoing COVID-19 pandemic is under-researched. Most, if not all, existing studies examinedthe disease contagion and shortage contagion separately,and did not take into consideration the dynamic inter-play between them. It is critical to characterize suchinterplay because the surging demand is caused by theepidemic arrival.In this paper, we develop a novel integrated networkmodel to examine the impacts of export restrictions onthe global PPE trade network during the COVID-19 pan-demic. We illustrate the structure of the model in Fig. 1.The proposed model integrates a susceptible-infected-recovered (SIR) based metapopulation model, which cap-tures the dynamics of disease contagion on the globalmobility network (top layer of Fig. 1), and a thresholdmodel, which captures the dynamics of shortage conta-gion on the global PPE trade network (bottom layer ofFig. 1). We investigate the shortage propagation pat-terns of eight sections of PPE commodities for five sce-narios on export restrictions. We provide quantitativeevidence that export restrictions cause shortage conta-gion to transmit even faster than that of the disease con-tagion. Besides, export restrictions delay the occurrenceof shortages for self-sufficient countries, but acceleratethe occurrence of shortages for not-self-sufficient coun-tries. In addition, export restrictions lead to ineffectiveand inefficient allocation of PPE worldwide.To capture the interplay between the disease contagionand the demand for PPE, we adapt a threshold model[14, 19] by (a) representing the increase of domestic de-mand for PPE as a result of the epidemic arrival, and (b)
DiseasContaShortage Contagion Increased demandNormal demandISR
FIG. 1. Overview of the integrated network model. The top(disease contagion) and bottom (shortage contagion) layersare the global mobility network where the epidemic spreads,and the global PPE trade network where the shortage con-tagion transmits, respectively. Nodes represent countries.Edges on the top layer represent the aggregated number ofseats on scheduled commercial flights between countries perday. Edges on the bottom layer represent the daily tradevalue between countries (in US dollars). Countries’ domesticdemand for PPE will increase since they are infected. adding an inventory module as the buffering mechanism.We construct the global PPE trade network using datafrom the United Nations Comtrade Database (UNCD)[21]. Here nodes represent countries and edges representthe annual trade value between countries (in US dollars).We select commodities with the World Customs Organi-zation’s Harmonized System codes for COVID-19 medi-cal supplies [22]. All commodities are classified into eightsections.Following Brockmann and Helbing [23], the SIR basedmetapopulation model is constructed based on the globalmobility network, which is defined by the daily air traf-fic data [24]. Here, nodes represent countries and edgesrepresent the aggregated number of seats on scheduledcommercial flights between countries. The populationdata used for constructing the global mobility networkis obtained from the United Nations World PopulationProspects national estimates [25]. After excluding thecountries that do not appear in these datasets, the pro-posed model has 195 countries.The model works on a daily time step. At time t ,each country i distributes its imports imp ( s ) i ( t ), produc-tion pro ( s ) i ( t ), and inventory inv ( s ) i ( t ) of commodities insection s to meet the domestic demand dem ( s ) i,dom ( t ) andforeign demand dem ( s ) i,for ( t ). We assume that domesticdemand has higher priority than foreign demand. Themaximum amount of commodities in section s that coun-try i can distribute at time t is D ( s ) i,max ( t ) = imp ( s ) i ( t ) + pro ( s ) i ( t ) + inv ( s ) i ( t ) . (1)If the epidemic arrives in country i at time t , the domes-tic demand for commodities in all sections will increase since then. Denote N i as the population size of coun-try i , and S i ( t ), I i ( t ), and R i ( t ) = N i − S i ( t ) − I i ( t ) asthe number of susceptible, infected, and recovered indi-viduals at time t , respectively. Then, following [23], thedynamics of disease contagion is given by ∂ t I i ( t ) = αS i ( t ) I i ( t ) σ ( I i ( t ) ǫN i ) N i − βI i ( t )+ γ X j = i P ji [ I j ( t ) − I i ( t )] ,∂ t S i ( t ) = − αS i ( t ) I i ( t ) σ ( I i ( t ) ǫN i ) N i + γ X j = i P ji [ S i ( t ) − S j ( t )] . (2)Here, α , β , γ , and ǫ are the infection rate, recovery rate,average mobility rate, and local invasion parameter, re-spectively. σ ( x ) = x η / ( x η + 1) is the sigmoid functionwith parameter η . Denote F ji as the number of pas-sengers traveling from country i to country j per day,and F i = P j F ji . Then P ji = F ji /F i is the fraction ofindividuals traveling from country i to country j , and P j P ji = 1. We obtain F ji by averaging the daily trafficdata on the global mobility network.Assuming that, before the pandemic, the domestic de-mand for commodities in section s is µ ( s ) i per capita perday for country i , thus, the total domestic demand forcommodities in section s for country i before the pan-demic is Dem ( s ) i = µ ( s ) i N i per day. We adopt the com-mon assumption that the domestic demand for PPE in-creases with the number of confirmed cases, and thenreaches a plateau. To capture this relationship, wemodify the relationship function in [26] and represent dem ( s ) i,dom ( t ) as dem ( s ) i,dom ( t ) = Dem ( s ) i [1 + θ d,i ( t )]= Dem ( s ) i + θ d,i ( t ) µ ( s ) i N i . (3)Here, θ d,i ( t ) is the demand increase factor for country i at time t , which is represented as follows. θ d,i ( t ) = k (
21 + e − k (cid:2) − Si ( t ) Ni (cid:3) − ) , (4)where k > θ d,i ( t ) and k > i ’s domestic demand (for commodities in section s ) fulfilled by i itself can be expressed as dem ( s ) i,dom,a ( t ) = min { D ( s ) i,max ( t ) , dem ( s ) i,dom ( t ) } . (5)Without export restrictions, the maximum foreign de-mand for commodities in section s to be fulfilled by coun-try i can be expressed as dem ( s ) i,for,max ( t ) = min { D ( s ) i,max ( t ) − dem ( s ) i,dom,a ( t ) ,dem ( s ) i,for ( t ) } . (6)Denote the proportion of commodities in section s beingexported from country i to country j as x ( s ) i,j = W ( s ) i,j Exp ( s ) i , (7)and we assume that x ( s ) i,j is constant. Here, W ( s ) i,j is theamount of commodities in section s that country i ex-ports to country j before the pandemic, and Exp ( s ) i ,country i ’s total exports of commodities in section s is Exp ( s ) i = X j W ( s ) i,j . (8) W si,j is obtained from the UNCD. Then, we can derivethe actual amount of commodities that country i exportsto country j at time t as w ( s ) i,j ( t ) = x ( s ) i,j dem ( s ) i,for,max ( t ) r i,j , (9)where r i,j ∈ { , } , and r i,j = 0 if country i restrictsexports to country j ; otherwise r i,j = 1. Thus, imp ( s ) j ( t + 1) = X i w ( s ) i,j ( t ) , (10)and the inventory of commodities in section s that coun-try i holds at the beginning of the next period (i.e., theend of the current period) is inv ( s ) i ( t + 1) = D ( s ) i,max ( t ) − dem ( s ) i,dom,a ( t ) − X j w ( s ) i,j ( t ) . (11)A lower inventory level than the initial level will resultin an increase in production, thus, the production at thenext period is decided as follows. pro ( s ) i ( t +1) = ( P ro ( s ) i inv ( s ) i ( t ) ≥ inv ( s ) i (0) ,P ro ( s ) i [1 + θ p,i ( t )] otherwise , (12)where θ p,i ( t ) is the production increase factor for coun-try i at time t . We assume that θ p,i ( t ) is non-negativefor the following reasons. During the pandemic, PPEproduction may decline due to the lockdown of cities,infection of workers, etc. But in the meanwhile, govern-ments have provided supports for PPE production andmanufacturers worldwide have retooled to produce morePPE to combat the pandemic. Therefore, we assume theproduction after the pandemic is no less than that beforethe pandemic.Assuming that countries cannot anticipate economicshocks, they issue orders to other countries at the end of each time period based on pro ( s ) i ( t + 1), dem ( s ) i,dom ( t ), and dem ( s ) i,for ( t ). The total amount of commodities in section s that country i orders from other countries is imp ( s ) i,o ( t ) =max { dem ( s ) i,dom ( t ) + dem ( s ) i,for ( t ) − pro ( s ) i ( t + 1) , } . (13)Denote the proportion of commodities in section s beingimported from country j to country i as y ( s ) j,i = W ( s ) j,i Imp ( s ) i , (14)and we assume that y ( s ) j,i is constant. Here, the totalamount of commodities in section s that country i im-ports from other countries is Imp ( s ) i = X j W ( s ) j,i . (15)Therefore, the amount of commodities that country i or-ders from country j is y ( s ) j,i imp ( s ) i,o ( t ), and dem ( s ) j,for ( t + 1) = X i y ( s ) j,i imp ( s ) i,o ( t ) . (16)We assume that, before the pandemic, Imp ( s ) i + P ro ( s ) i = Exp ( s ) i + Dem ( s ) i . (17)We initialize the model by setting pro ( s ) i (0) = P ro ( s ) i , imp ( s ) i (0) = Imp ( s ) i , and dem ( s ) i,for (0) = Exp ( s ) i . We as-sume that inv ( s ) i (0) = φ ( s ) i Imp ( s ) i . (18)This assumption means that country i can still meet thedomestic demand and foreign demand without importsfor φ ( s ) i days before the pandemic.In the simulations, we consider the simplest pandemicscenario, where no travel bans or other public health mea-sures are considered. For simplicity, we assume k = 2, k = 100, and µ si = 10 for all countries and all com-modities. Following epidemiology literature, the meaninfectious period is set as 4.6 days [27] leading to therecovery rate β = 0 . R is set as 2.6 [28], leading to the infection rate α = R β = 0 . γ is estimated to be 0 . ǫ and η in [23], ǫ = 10 − and η = 8.We set that China is initially infected with 100 infectedcases at t = 0, which corresponds to December 31, 2019,the date when the World Health Organization was in-formed of unknown pneumonia cases detected in Wuhan,China [29]. We run the simulation for one year.Now, we model five different export restriction scenar-ios among countries, and present their impacts on the TABLE I. Description of five export restriction scenarios.Scenario DescriptionS none
No country restricts exportsS The largest exporter restricts exportsS The top 5% of exporters restrict exportsS lower
The lower half (50%) of exporters restrict exportsS all
All countries restrict exports trade network for each commodity section. The descrip-tion of each scenario is given in Table I. For the rest ofthis paper, we only present the numerical results for com-modities in section 1 (COVID-19 test kits and apparatusused in diagnostic testing) and section 2 (protective gar-ments and the like), because they represent two typicalsituations: (a) the initially infected country (China) isnot the largest exporter (Germany) in section 1, and (b)the initially infected country (China) is also the largestexporter in section 2. Results for other sections are con-sistent with the results for these two sections, and thusare presented in the Supplemental Material. D E U C H E U S A I R L B E L O t h e r (a) Section 1 C H N D E U U S A M Y S I T A O t h e r (b) Section 2 20%40%60%80%100% D a il y e x p o r t s C u m u l a t i v e p e r c e n t a g e FIG. 2. The Pareto distribution in global exports. The dailyexports (left) and the cumulative percentage of daily globalexports (right) in (a) section 1 and (b) section 2 for the topfive exporters and other countries. DEU = Germany, CHE= Switzerland, USA = the United States of America, IRL =Ireland, BEL = Belgium, CHN = China, MYS = Malaysia,ITA = Italy.
First, we give an overview of the trade network forsection 1 and section 2. In Fig. 2, we present the dailyexports and the cumulative percentage of daily global ex-ports in section 1 and section 2 for the top five exportersand other countries. We observe a Pareto distributionin global exports in Fig. 2, where the top five exportersshare about 70% and 52% of global exports in section 1and section 2, respectively.In Fig. 3, we plot the number of infected countriesand the number of countries facing shortages at the endof each month in different scenarios. Country i willface shortages of commodities in section s at time t ifits domestic demand cannot be met, i.e., D ( s ) i,max ( t ) Scenario S Scenario S Scenario S lower Scenario S all Infected J a n M a r M a y J u l S e p N o v (b) Section 2 FIG. 3. The number of infected countries and the numberof countries facing shortages of commodities in (a) section 1and (b) section 2 at the end of each month. The descriptionof scenarios is given in Table I. Parameters are set as follows: θ p,i ( t ) = 0, φ ( s ) i = 10. all scenarios. Generally, export restrictions exacerbateglobal supply shortages. We can observe that, com-pared with scenario S all where all countries restrict ex-ports, the number of countries facing shortages decreasesgreatly in the early periods (from January to June) inscenario S none where no country restricts exports. Be-sides, the number of countries facing shortages in scenario S (only the top 5% of exporters restrict exports) isnearly the same as scenario S all , which can be explainedby the Pareto distribution in global exports. Counter-intuitively, the number of countries facing shortages inscenario S lower (the lower half of the exporters restrictexports) is slightly fewer than that in scenario S none .The reason is as follows. The total percentages of worldexports that the lower half of the exporters share areonly 0.005% and 0.053% for section 1 and section 2, re-spectively. They can hardly help other countries man-age supply shortages. Besides, exports lower the inven-tory level of these countries, thus, in scenario S lower , re-stricting exports can delay the shortages when diseasearrives at these countries. These findings show that, onthe one hand, agreements are urgently needed to ensureopen trade between countries during the pandemic; onthe other hand, such agreements should also allow coun-tries that contribute little to global exports to imposesome export restrictions in order to ensure a sufficientinventory for the upcoming pandemic.For section 1, we find that scenario S leads to manymore countries facing shortages as compared to scenario S none , because Germany (the largest exporter) stops sup-plying commodities to others. This gap shrinks for sec-tion 2, because the largest exporter (China) is the ini-tially infected country as well. So even without export re-strictions (such as scenario S none ), China has to meet thedomestic demand by lowering the exports significantly.Moreover, we find that for both sections, there are morecountries facing shortages than infected countries in sce-narios S , S , and S all . This finding indicates thatpandemic-resulted export restrictions can make shortagecontagion transmit even faster than disease contagion. DEU CHEUSA IRLBEL (a) Section 1, Scenario S none DEUCHEUSA BEL (b) Section 1, Scenario S all CHN DEUUSAMYS ITA (c) Section 2, Scenario S none CHN DEUUSAMYS ITA (d) Section 2, Scenario S all Self-sufficient Not-self-sufficient T a [days] T s [ d a y s ] FIG. 4. Comparison of the epidemic arrival time T a and thefirst shortage time T s for each country in (a) section 1, sce-nario S none , (b) section 1, scenario S all , (c) section 2, scenario S none , and (d) section 2, scenario S all . Nodes represent coun-tries. The size of a node represents the export value of com-modities in the corresponding section. The color of a nodeindicates if it is a self-sufficient country for the section. Theblue line corresponds to T a = T s . Parameters are set as fol-lows: θ p,i ( t ) = 0, φ ( s ) i = 10. For clarity, only the top fiveexporters are presented with the three-letter country code.DEU = Germany, CHE = Switzerland, USA = the UnitedStates of America, IRL = Ireland, BEL = Belgium, CHN =China, MYS = Malaysia, ITA = Italy. Next, we compare the epidemic arrival time T a and thefirst shortage time T s for each country in different scenar-ios. We present the results for scenarios S none and S all in Fig. 4. Note that countries not facing shortages withinthe simulation periods are not represented in Fig. 4. Theepidemic arrival time T a is defined as the date of the firstinfected case after the initial outbreak. The first short-age time T s is defined as the date when a country firstfaces PPE shortages. Nodes represent countries. Thesize of a node represents the export value of commodi-ties in the corresponding section. The color of a nodeindicates if it is a self-sufficient country for the section.Country i is self-sufficient for commodities in section s when its production is no less than its domestic demandbefore the pandemic, i.e., P ro ( s ) i > = Dem ( s ) i . The blueline corresponds to T a = T s . If a country faces shortagesbefore infected, it locates below the blue line. Otherwise,it locates above the blue line.As illustrated in Fig. 4 (a) and Fig. 4 (b), we can ob-serve in section 1 that, compared with scenario S all , morenot-self-sufficient countries locate above the blue line inscenario S none . The fraction of not-self-sufficient coun-tries above the blue line increases to 65% in scenario S none from 1% in scenario S all . In section 2, we alsoobserve that export restrictions lead to a much earlieroccurrence of shortages for not-self-sufficient countries inFig. 4 (c) and Fig. 4 (d). The mean value of T s decreasesto 22 days in scenario S all from 105 days in scenario S none . In Fig. 5, we also present the fraction of countrieswith T s > T a in section 1 and the mean value of T s insection 2 for not-self-sufficient countries in all scenarios.The differences in scenarios are consistent with that inFig. 3. To sum up, when all countries restrict exports, al-most all not-self-sufficient countries locate below the blueline, which can be observed in both section 1 and section2, indicating that they encounter PPE shortages evenbefore the epidemic arrival. Besides, both self-sufficientcountries and not-self-sufficient countries locate fartheraway from each other in scenario S all than in scenario S none . Similar results to scenario S all are found in sce-nario S and scenario S . These results indicate thatexport restrictions delay the occurrence of shortages forself-sufficient countries, but accelerate the occurrence ofshortages for not-self-sufficient countries. S none S S S lower S all F r a c t i o n o f c o un t r i e s w i t h T s > T a 65% 4% 1% 78% 1% (a) Section 1 S none S S S lower S all M e a n v a l u e o f T s [ d a y s ] 105 45 19 118 22 (b) Section 2Scenario FIG. 5. (a) Fraction of not-self-sufficient countries with T s >T a in section 1 and (b) the mean value of T s in section 2 fornot-self-sufficient countries in all scenarios. Parameters areset as follows: θ p,i ( t ) = 0, φ ( s ) i = 10. These results also present the double-edged natureof the PPE trade relationship between countries. Onthe one hand, such relationships allow countries (espe-cially not-self-sufficient countries) to address the pan-demic with the help of trading partners. On the otherhand, shortage contagion can also transmit through theserelationships. As illustrated in Fig. 4(c), 80 countries suf-fer from shortages while only 26 countries are infected at t = 100. The surge in domestic demand in infected coun-tries leads to a reduction in their exports. The shortagecontagion then spills over to non-infected countries be-cause the domestic demand cannot be met. However,countries can mitigate such spillover effects by increas-ing production while facing shortages. We present theaveraged fraction of countries facing shortages for eachmonth with different production increase factor θ p,i ( t ) inscenarios S none and S all in the Supplemental Material.We observe in both sections that, the number of countriesfacing shortages decreases greatly as θ p,i ( t ) grows, espe-cially at the early stage (from January to June). Besides,even as θ p,i ( t ) grows, there are still more countries fac-ing shortages in scenario S all than that in scenario S none for the same θ p,i ( t ). These results indicate that cooper-ation between countries (no export restrictions) alwaysplays an essential role in preventing global shortages ofPPE regardless of the production level. But at the sametime, a higher production level leads to less dependenceon imports, which greatly helps countries cope with PPEshortages. Therefore, except for promoting global co-operation, governments and international organizationsshould take actions to reduce supply chain barriers andwork together to increase global PPE production.Finally, we compare the world total inventory Inv ( s ) w ( t )and the world total unmet domestic demand U ( s ) w ( t ) forboth sections at the end of time t . We define Inv ( s ) w ( t )= P i inv ( s ) i ( t + 1) and U ( s ) w ( t ) = P i dem ( s ) i,dom ( t ) − dem ( s ) i,dom,a ( t ). We present the average values of Inv ( s ) w ( t )and U ( s ) w ( t ) from January to June in Fig. 6. If Inv ( s ) w ( t ) > 0, the world total inventory level Inv ( s ) w ( t ) and the worldtotal unmet domestic demand U ( s ) w ( t ) in scenarios S none , S , and S lower are all lower than that in scenarios S and S all . Compared with scenario S all , U ( s ) w ( t ) in sce-nario S none is reduced by 100%, 93%, and 24% for Jan-uary, February, and March in section 1, respectively. Insection 2, U ( s ) w ( t ) is reduced by 100%, 100%, and 0.64%for January, February, and March, respectively. These re-sults show that, with export restrictions, a large amountof PPE is hoarded instead of being distributed to whereit is most needed, particularly at the early stage. Wecan also find that, although there are more countries fac-ing shortages in scenario S than that in scenario S all (Fig. 3), Inv ( s ) w ( t ) and U ( s ) w ( t ) in scenario S are almostthe same as or even slightly lower than that in scenario S all . From this perspective, we can conclude that themore top exporters restrict exports, the less effective theglobal PPE supply chain is. These findings further indi-cate that export restrictions are not an appropriate so-lution to address the pandemic. A fully functional PPEsupply chain system could leave countries more time toadapt their production and identify alternative supplysources. Countries should lift the export restrictions tohelp allocate PPE more effectively and efficiently for thecollective benefit of humankind.In summary, we investigated how the shortage conta-gion, induced by demand surges and export restrictions,transmits on the global PPE trade network during theCOVID-19 pandemic. We simulated the impacts of fiveexport restriction scenarios based on an integrated net-work model, which integrates the real-world PPE tradedata and global mobility data. We find evidence thatthe shortage contagion pattern is mainly determined bythe export restriction policies of the top exporters. Ex-port restrictions can cause shortage contagion to trans- (a) Section 1, Inv w (b) Section 1, U w J a n F e b M a r A p r M a y J un (c) Section 2, Inv w J a n F e b M a r A p r M a y J un (d) Section 2, U w Scenario S none Scenario S Scenario S Scenario S lower Scenario S all FIG. 6. Average world total inventory Inv ( s ) w ( t ) (a, c) andworld total unmet domestic demand U ( s ) w ( t ) (b, d) of section1 (a, b) and section 2 (c, d) from January to June in allscenarios. Parameters are set as follows: θ p,i ( t ) = 0, φ ( s ) i = 10 mit even faster than the disease contagion, with only thetop 5% of exporters imposing export restrictions. Tosome extent, export restrictions can provide benefits forself-sufficient countries, at the sacrifice of immediate eco-nomic shocks at not-self-sufficient countries. The resultsalso validate that export restrictions are not an effectiveand efficient solution to confront the pandemic. PPE isnot properly allocated to countries with shortages. Tobetter respond to the next wave of COVID-19 and otheremerging infectious diseases, countries should keep PPEtrade open and reduce reliance on only a small numberof PPE exporters. ∗ [email protected][1] WHO, Coronavirus disease (COVID-19) Weekly Epidemiological Update and Weekly Operational Update (2020), . who . int/emergencies/diseases/novel-coronavirus-2019/situation-reports .[2] Q. Li, X. Guan, P. Wu, X. Wang, L. Zhou, Y. Tong,R. Ren, K. S. Leung, E. H. Lau, J. Y. Wong, et al. , NewEngland Journal of Medicine (2020).[3] R. M. Anderson, H. Heesterbeek, D. Klinkenberg, andT. D. Hollingsworth, The Lancet , 931 (2020).[4] G. He, Y. Pan, and T. Tanaka, Nature Sustainability ,1 (2020).[5] D. Laborde, W. Martin, J. Swinnen, and R. Vos, Science , 500 (2020).[6] WTO, WTO report finds growing number of export restrictions in response to COVID-19 crisis (2020), . wto . org/english/news e/news20 e/rese 23apr20 e . htm .[7] C. P. Bown, COVID-19 and Trade Policy: Why TurningInward Won’t Work , 31 (2020).[8] T. Burki, The Lancet Infectious Diseases , 785 (2020).[9] N. J. Rowan and J. G. Laffey, Science of The Total En-vironment , 138532 (2020).[10] C.-Y. Park, K. Kim, and S. Roth, (2020).[11] J. Pauwelyn, Available at SSRN 3579965 (2020).[12] D. Guan, D. Wang, S. Hallegatte, S. J. Davis, J. Huo,S. Li, Y. Bai, T. Lei, Q. Xue, D. Coffman, et al. , NatureHuman Behaviour , 1 (2020).[13] L. Wenz and A. Levermann, Science advances , e1501026 (2016).[14] R. Burkholz and F. Schweitzer, Environmental ResearchLetters , 114013 (2019).[15] J. A. Gephart, E. Rovenskaya, U. Dieckmann, M. L.Pace, and ˚A. Br¨annstr¨om, Environmental Research Let-ters , 035008 (2016).[16] T. Distefano, F. Laio, L. Ridolfi, and S. Schiavo, PloSone , e0200639 (2018).[17] S. V. Buldyrev, R. Parshani, G. Paul, H. E. Stanley, andS. Havlin, Nature , 1025 (2010).[18] M. G. A. Contreras and G. Fagiolo, Physical Review E , 062812 (2014).[19] D. J. Watts, Proceedings of the National Academy ofSciences , 5766 (2002).[20] D. Centola, V. M. Egu´ıluz, and M. W. Macy, PhysicaA: Statistical Mechanics and its Applications , 449(2007). [21] UN, UN comtrade (2018), https://comtrade . un . org/ .[22] WCO, New edition of the WCO/WHO HS Classification List for COVID-19 Medical Supplies now available (2020), . wcoomd . org/en/media/newsroom/2020/june/new-edition-of-the-wco-who-hs-classification-list-for-covid-19-medical-supplies-now-available . aspx .[23] D. Brockmann and D. Helbing, science , 1337 (2013).[24] OAG, (2013), . oag . com/ .[25] UN, United Nations World Population Prospects (2013), https://population . un . org/wpp/ .[26] C. J. Worby and H.-H. Chang, Nature communications , 4049 (2002).[27] S. M. Moghadas, A. Shoukat, M. C. Fitzpatrick, C. R.Wells, P. Sah, A. Pandey, J. D. Sachs, Z. Wang, L. A.Meyers, B. H. Singer, et al. , Proceedings of the NationalAcademy of Sciences , 9122 (2020).[28] J. Riou and C. L. Althaus, Eurosurveillance , 2000058(2020).[29] WHO, Archived: WHO Timeline - COVID-19 (2020), . who . int/news/item/27-04-2020-who-timeline---covid-19int/news/item/27-04-2020-who-timeline---covid-19