Supply chain loss from easing COVID-19 restrictions: an evolutionary economic-epidemiological modelling study

Since the start of the COVID-19 pandemic, many firms have been shifting their supply chains away from countries with stringent control measures to mitigate supply-chain disruption. Nowadays, the global economy has reopened from the COVID-19 pandemic at various paces in different countries. Understanding how the global supply network evolves during and after the pandemic is necessary for determining the timing and speed of reopening. By harnessing the real-world and real-time global human movement and the latest macroeconomic data, we propose an evolutionary economic-epidemiological model to explore the evolutionary dynamics of the global supply network under various global reopening scenarios. We find that, for highly restrictive countries, the delay in reopening has limited public health benefits in the long run but leads to significant supply-chain loss. A longer duration of stringent control measures substantially hurts the profitability of firms in highly restrictive countries, leading to slower supply-chain recovery in 5 years. This research presents the first data-driven evidence of supply chain loss due to the timing and speed of reopening and sheds light on the post-pandemic supply-chain reformation and recovery. Insights learned from COVID-19 will also be a valuable policymaking reference for combating future infectious disease epidemics and geopolitical changes.

Since the start of the COVID-19 pandemic, many firms have been shifting their supply chains away from countries with stringent control measures to mitigate supply-chain disruption.Nowadays, the global economy has reopened from the COVID-19 pandemic at various paces in different countries.Understanding how the global supply network evolves during and after the pandemic is necessary for determining the timing and speed of reopening.By harnessing the real-world and real-time global human movement and the latest macroeconomic data, we propose an evolutionary economic-epidemiological model to explore the evolutionary dynamics of the global supply network under various global reopening scenarios.We find that, for highly restrictive countries, the delay in reopening has limited public health benefits in the long run but leads to significant supply-chain loss.A longer duration of stringent control measures substantially hurts the profitability of firms in highly restrictive countries, leading to slower supply-chain recovery

Introduction
The unprecedented control measures for the coronavirus disease 2019 (COVID-19) pandemic [1] have been proven effective [2][3][4] but at the cost of enormous social and economic disruptions [5][6][7][8].With the increasing population immunity by vaccinations and infections, most countries have been gradually lifting COVID-19 restrictions and reopening society and the economy since late 2021 [9,10].The pace of reopening varies widely across the world.Many European countries have lifted nearly all COVID-19 restrictions and returned to pre-pandemic normalcy in late 2021 [11,12].At the same time, some Asian countries, such as China, continued maintaining stringent containment measures, aiming at stamping out outbreaks as soon as they arise [13,14].On 11 November 2022, China announced 20 new guidelines for easing the 'Zero COVID' policy [15], marking the start of shifting from the zero-COVID policy, yet the economy has not fully recovered.
The reopening pace of a country affects both domestic and global economic recovery, as economic disruption can propagate across borders through the global supply network [16][17][18].Many firms have been shifting their supply chains towards less restrictive countries to reduce the risk of supply disruption and ensure comprehensive recovery [19][20][21].Highly restrictive countries may suffer shrinking revenue and loss of market share due to supply-chain shifting, while less restrictive countries may attract more investment and gain market share from competitors.However, it remains unclear whether the temporary supply-chain shifts will become permanent and how the global supply network will evolve during and after the pandemic under different global reopening scenarios.
Existing literature extensively explores the impacts and management strategies of supplychain disruptions caused by various factors [22][23][24][25][26][27], such as natural disasters [28], demand fluctuations [29] and intentional attacks [30].Pandemic-induced disruptions, characterized by the unpredictable nature, prolonged duration and simultaneous impacts on the supply and demand sides, pose major challenges for business operations and public health policy-making [31][32][33].Our understanding of pandemic-induced disruptions has been significantly expanded, especially since the COVID-19 pandemic [34][35][36][37].One branch of the literature proposes efficient and resilient risk-mitigation strategies in the face of supply-chain disruptions [38][39][40].Various conceptual [41][42][43] and analytical models [44][45][46] have been developed to help guide disruption management and decision-making amid pandemic-induced supply-chain uncertainty.Another branch of literature, pertinent to our study, aims to measure the impact of the pandemic on supply chains [16,35,47], such as food [48,49], personal protective equipment [18], agriculture [50] and lightning equipment supply chains [33].Simulation models [16,18,33,51] are essential tools for evaluating supply-chain performance during and post-pandemic.Owing to the scarcity of extensive firm-level supply-chain data, firm-level models rely on hypothetical firm networks or are restricted to the supply-chain network featuring a few industries or firms.To simulate and estimate the effects of pandemic-induced disruptions on large-scale supply-chain networks and the economy, adaptive economic models based on inter-sector input-output tables have been widely used as alternatives [16,[52][53][54][55][56][57][58].
However, previous adaptive input-output economic models that investigated the global supply-chain effects of COVID-19 restrictions [16,58] only considered their short-term effects.In other words, although these models consider the reallocation of orders between suppliers and the expansion or contraction of firms' production in response to downstream demand changes [59,60], these adjustments will not hurt the competitiveness of firms.Therefore, in these models, firms' production will fully resume to pre-pandemic levels instantaneously when the pandemic ends.While these assumptions are acceptable in analysing the effects of short-term COVID-19 restrictions, they are unrealistic if the restrictions last for years because firms cannot survive in the long run without making profits, and unprofitable firms may permanently lose market share to highly profitable ones in a competitive business environment.A few small-scale studies focusing on the policy analysis of a specific region consider upsizing (downsizing) the workforce of firms with rising (declining) profits [54,61,62].However, the evolution of global supply chains under the competition of firms in the global market is still unclear.Understanding the reformation and recovery of global supply chains during and after the pandemic can help examine the cost of pandemic restrictions and facilitate the determination of reopening timing and speed.The insights learned from COVID-19 will be a valuable policymaking reference for combating future infectious disease epidemics and geopolitical changes.
To address this gap, we develop an evolutionary economic-epidemiological model to investigate the short-term and long-term supply chain impacts of different global reopening scenarios.The model integrates a meta-population epidemiological model and an evolutionary multi-regional input-output (MRIO) economic model.The epidemiological model simulates the transmission dynamics of COVID-19 and characterizes the changes in the stringency of COVID-19 restrictions in response to epidemic situations.The economic model characterizes the supply chain shifts due to the competition between firms based on Fisher's fundamental theorem of natural selection [63,64].Under the supply and demand constraints determined by the epidemiological model, the economic model projects the global trade flows between firms in different global reopening scenarios.We illustrate the model scheme in figure 1.A detailed description of the model is provided in the Methods.

Methods (a) SVEIRD-based meta-population model
We simulate the transmission dynamics of COVID-19 across countries based on the SVEIRDbased meta-population model proposed in our previous study [65].Individuals in country i are divided into the following classes: susceptible individuals (S i ), vaccinated individuals (V i ), exposed individuals (not yet infectious) without vaccinal immunity (E S i ), exposed individuals (not yet infectious) with vaccinal immunity (E V i ), infectious individuals without vaccinal immunity (I S i ), infectious individuals with vaccinal immunity (I V i ), recovered individuals (R i ) and deceased individuals (D i ).
Similarly, the transition rate from V i to E V i is Susceptible individuals are vaccinated at the vaccination rate φ i (t).We assume vaccinated individuals gradually lose vaccinal immunity and become fully susceptible again at the rate ε.
An exposed individual has a transition rate σ to become infectious.An infectious individual has a transition rate α to become either recovered or deceased.For individuals without vaccinal immunity, the transition rates from infectious to recovered and deceased are (1 − ν)α and να, respectively; for individuals with vaccinal immunity, the transition rates from infectious to recovered and deceased are [1 − (1 − )ν]α and (1 − )να, respectively.Here, ν is the severity of the virus.Recovered individuals may lose their natural immunity and acquire the virus again at rate ψ.Thus, the duration of natural immunity is 1/ψ.The natural birth rate and the natural mortality rate for country i are denoted by ζ i (t) and υ, respectively.We assume that without COVID-19, the population size for all countries will not change during the simulation period.Thus, . Denote the number of individuals travelling between country i and country j at time t as G ij (t).We assume deceased individuals do not travel across countries.The disease transmission dynamics are described by the following equations: A detailed description of parameter settings can be found in electronic supplementary material, note S2.

(b) Evolutionary MRIO model
We extend previous adaptive multi-regional input-output models [16,66,67] by (i) integrating the economic model with an epidemiological model to predict dynamic supply and demand constraints under different reopening policies and (ii) modelling the change in firms' production capacity in an endogenous manner based on Fisher's fundamental theorem of natural selection [63,68,69] from evolutionary economics.The global supply network is constructed using data from the latest version of the Global Trade Analysis Project database (GTAP 10) [70].GTAP 10 provides an MRIO table for the year 2014, representing the annual monetary transactions between 65 sectors of 141 countries.For each country, we treat each sector as a representative firm and the entire final demand system as a representative household.A firm is represented by the index pair ai, where a denotes the products produced by the firm and i denotes the region in which the firm is located.Each node on the global supply network represents a firm or a representative household.An edge between two nodes represents the trade flows between them.A graphical illustration of the global supply-chain network can be found in electronic supplementary material, figure S26.Each firm uses primary production factors (for simplicity, we only consider labour in the model) and domestic and foreign intermediate products to produce a specific product.Denote the maximum labour input for firm ai at time t as L ai (t), then where L * ai is the labour input for firm ai before the pandemic; κ ai (t) ≥ 0 is the production adjustment ratio, representing the expansion [κ ai (t) > 1] or contraction [κ ai (t) < 1] of production for firm ai at time t; r ai (t) is the fraction of workers who are unable to work due to illness or COVID-19 restrictions (such as the closure of workplaces).We define ) ] is the impact-to-labour multiplier for sector a.We neglect death-induced labour unavailability since not many work-age individuals die from COVID-19.Denote the set of intermediate products for firm ai as P ai .For intermediate product b ∈ P ai , the inventory that firm ai holds at the end of time t − 1 and the amount arrived at firm ai from firm bj at time t are represented by Inv b ai (t − 1) and PTF bj→ai (t), respectively.Then, the maximum output of firm ai at time t can be expressed by the following Leontief production function [71]: where q L ai = L * ai /x * ai and q b ai = j Z * bj→ai /x * ai are the input coefficients.Here, x * ai and Z * bj→ai are the output of firm ai and the trade flow from firm bj to firm ai before the pandemic, respectively.The actual output of firm ai depends on its maximum output and its orders from clients, which is represented as x A ai (t). (2.8) The amount of product a arrived at the household in country j from firm ai is x A ai (t). (2.9) The inventory of intermediate product b that firm ai holds at the end of time t is In a competitive business environment, firms with higher profitability can attract more investment and push weak competitors out of the market.We model the competition between firms based on Fisher's fundamental theorem of natural selection, which, in economic terms, states that the rate of change in average profitability in a population of competing firms is governed by profitability differentials among these firms.We assume that firms producing the same product (i.e. in the same sector) are competing firms.Then, following Fisher's fundamental theorem, M ai (t) is the market share of firm ai in sector a at time t, which is defined as . (2.12) is the production level of firm ai at time t.We assume that the total production level of firms in the sector is constant, then j xaj (t) = j x * aj .ξ ai (t) is the profitability of firm ai, which assesses its ability to generate profits based on its resources.We define the profitability of firm ai at time t as implying that firms carrying excess capacity (i.e. the demand a firm receives is less than its production level) and making less efficient use of resources have weak profitability [72].ξ a (t) = j ξ aj (t)M aj (t) is the average profitability among firms in sector a at time t.ρ is the rate of evolutionary change.ξ ai (t) = ξ ai (t) − ξ a (t) is the variation in profitability of firm ai at time t, indicating the difference of its profitability from the average value.Thus, the production expansion ratio for firm ai at time t + 1 is Denote the market structure change over the projection horizon for sector a as M a .We define Assuming that each firm issues orders from its suppliers to meet the demand for the intermediate products based on the suppliers' latest production level and reliability.Following [66], we define the reliability of firm ai at time t as with the discounting factor ϕ. The order issued by firm ai to firm bj at time t is The demand for product b for the household in country i at time t depends on the pandemic situation in country i.Following [58], we define (2.20) Here, DemH b * i = j y * bj→i is the demand of product b for the household in country i before the pandemic; y * bj→i is the trade flow from firm bj to the household in country i before the pandemic; ϑ D b is the impact-to-demand multiplier, representing the utmost demand change of product b for households during the pandemic.Similarly, each household issues orders to firms based on their latest production level and reliability.Therefore, the order issued by the household in country i to firm bj at time t is A detailed description of parameter settings can be found in electronic supplementary material, note S2.

Results (a) Disease transmission dynamics under different global reopening scenarios
For consistency, we simulate the transmission dynamics of COVID-19 under different hypothesized global reopening scenarios over a 5-year projection horizon starting from 1 March 2022, when the Omicron variants' frequency reached over 95% worldwide.We model three global reopening scenarios differentiated by the timing and speed of reopening paths, namely, the explosive, steady and incremental reopening scenarios.Specifically, there will be no COVID-19 restrictions in all countries/regions (for simplicity, we use 'countries' in the following discussion) in 12 months (explosive) and 18 months (steady and incremental) since 1 March 2022.Under the explosive reopening scenario, a country will maintain certain containment measures before full reopening.While under the steady and incremental reopening scenarios, a country will gradually lift the remaining containment measures until it fully reopens.Containment measures are lifted at constant and accelerating speeds under the steady and incremental reopening scenarios, respectively.The settings in these hypothesized reopening scenarios reflect two typical control (a)   -e) and cumulative mortality rate (f-i) in all (b,f ), high-CHI (e,g), mid-CHI (d,h) and low-CHI (e,i) countries/regions under different global reopening scenarios.Dotted, dashdotted and solid lines correspond to the results under the explosive, steady, and incremental reopening scenarios.Owing to the high prevalence rate in the first year, we only present the results from the second year of the projection horizon in the main text for clear illustration.Results for the whole projection horizon are presented in electronic supplementary material, figure S1.
strategies in the real world [16,73]: maintaining strict policies for a shorter period or relaxing strict policies but keeping restrictions in place for a longer period.The stringency of COVID-19 restrictions in each country before full reopening is measured based on the Containment and Health Index (CHI) by the Oxford COVID-19 Government Response Tracker [74] (electronic supplementary material, Note 1).We classify countries into three groups according to their CHI scores on 1 March 2022 (t = 0): high-CHI, mid-CHI and low-CHI, as shown in figure 2a. Figure 2b-i presents the average prevalence and cumulative mortality rate in all, high-CHI, mid-CHI and low-CHI countries over the projection horizon.Due to the high transmissibility of the Omicron variants [75] and limited vaccine efficacy against infections [76], relying solely on vaccines cannot contain the spread of the virus.Consequently, lifting COVID-19 restrictions brings a surge in infection under all reopening scenarios.This surge is more significant in high-CHI countries because of limited previous exposure to the virus.This rapid surge of COVID-19 infections following the reopening is anticipated to result in short-term and high-impact disruptions to supply chains, especially for high-CHI countries under the explosive reopening scenario.Effective mitigation strategies, such as strategic inventory management, proactive communication with suppliers and clients, and optimizing distribution networks, are essential for supply chains to enhance resilience and efficiency in the crisis.Although the virus cannot be eradicated, the subsequent spikes become smaller, and the pandemic becomes an endemic eventually.Different reopening strategies result in similar epidemic trajectories.The cumulative mortality rates under the explosive and incremental reopening scenarios are almost the same over the projection horizon and slightly lower than the rate under the steady reopening scenario.The widespread outbreak is inevitable regardless of the timing and speed of reopening.The COVID-19 pandemic has shown a recurring pattern of surges and declines, which requires the development of more resilient healthcare supply chains that can quickly and flexibly cope with demand fluctuations and adapt capacity to meet the needs of future waves.

(b) Supply chain impacts of different global reopening scenarios
Implementing COVID-19 restrictions slows the spread of infection but comes at economic costs caused by disrupted economic activities in production sectors (hereafter, sectors).We measure the supply-chain impact of different global reopening scenarios on a specific sector as the change in its gross value added (GVA) relative to pre-pandemic levels.The GVA change may be directly induced by the reduced labour availability due to illness or COVID-19 restrictions (pandemicinduced GVA change), or indirectly induced by the supply disruption due to (a) shortages of intermediate inputs (supply disruption-induced GVA change) or (b) the expansion/contraction of production due to competition between firms (competition-induced GVA change).The total GVA change is the sum of pandemic-induced, supply disruption-induced and competition-induced GVA change.The GVA of a country is the sum of the GVA of all sectors.See Methods and electronic supplementary material, Note 3 for detailed definitions.
Figure 3 shows the GVA change in all, high-CHI, mid-CHI, and low-CHI countries under different global reopening scenarios.There are almost consistently negative total GVA changes in high-and mid-CHI countries before full reopening.The decomposition of the total GVA loss indicates that the pandemic-induced GVA loss, mainly due to COVID-19 restrictions, contributes significantly to the total GVA loss.As COVID-19 restrictions continue, supply disruption propagates along the global supply network, driving up the contribution of supply disruptioninduced GVA loss to the total GVA loss.To withstand supply disruption in countries imposing strict restrictions, firms shift supply chains to less restrictive countries, leading to the expansion (contraction) of production in less (highly) restrictive countries.High-CHI countries suffer the most from supply chain shifting, where the competition-induced GVA change is negative and continuously declines over the restriction period.The competition-induced GVA change is almost unchanged in mid-CHI countries but steadily grows in low-CHI countries, indicating that the majority of supply chains shifting away from high-CHI countries are absorbed by low-CHI countries.
Lifting COVID-19 restrictions leads to a recovery in production levels in all firms but will not resume the global supply network to the pre-pandemic state immediately.When the world fully reopens, the pandemic-induced and supply disruption-induced GVA loss will diminish quickly.The competition-induced GVA change resumes much slower and becomes the dominant part of the total GVA change.Sustained competition-induced GVA loss in high-CHI countries indicates that supply chains that previously shifted away from high-CHI countries will not completely shift back in the short term.High-CHI countries suffer permanent GVA loss at the end of the projection horizon, which is mostly absorbed by low-CHI countries.Although the world fully reopens earlier under the explosive reopening scenario than the steady and incremental reopening scenarios, the back-shifting process is the slowest under the explosive reopening scenario.Moreover, compared to the incremental reopening scenario, steady reopening leads to smaller competition-induced GVA changes over the projection horizon.These results demonstrate that supply-chain shifting is mainly driven by the imposition of strict policies.Faster relaxation of strict policies leads to slower supply-chain shifting, even if restrictions remain in high-CHI countries ( f ) Figure 3. Supply chain impacts of different global reopening scenarios.The total, pandemic-induced, supply disruptioninduced and competition-induced gross value added (GVA) change relative to pre-pandemic levels in all (blue; a-c), high-CHI (red; d-f ), mid-CHI (orange; g-i), and low-CHI (green; j-l) countries under different global reopening scenarios.The first, second and third columns correspond to the results under the explosive, steady and incremental reopening scenarios, respectively.The grey area and the solid grey line indicate the restriction period and the end of the restriction period.The grey dashed line indicates the pre-pandemic level.The total, pandemic-induced, supply disruption-induced and competitioninduced GVA change are represented by shaded areas, solid, dotted and dash-dotted lines, respectively.
place for longer.This is in line with the previous finding that a gradual and long-term recovery plan results in significantly lower economic loss than a short-term but strict one [16].

(c) Competition between firms leads to supply-chain loss in the long run
Different sectors undergo heterogeneous global market structure changes in the reopening process.The market structure of a sector is defined as the distribution of market share among firms in this sector [77].We define a firm's market share as its share of the global production of the sector it belongs to. Figure 4 shows the changes in the market structure of ten sectors over the projection horizon under different global reopening scenarios.These sectors have varying impact-to-production multipliers (capturing the effects of COVID-19 restrictions on production; see Methods) and impact-to-demand multipliers (capturing the impact of disease dynamics on final demand; see Methods).Results for other sectors are presented in electronic supplementary material, figures S2-S13.For comparison, we present the changes in market share relative to prepandemic levels for the ten largest producers (countries) at two special timestamps: the end of the restriction period and the end of the projection horizon.Consistent with the results in figure 3, steady reopening leads to the smallest changes in market structures for all sectors.Generally, the market structure changes are similar under the explosive reopening and the incremental reopening scenarios except for a few sectors, such as the coal sector (COA), where explosive reopening leads to significantly larger market structural changes than incremental reopening.Sectors where production hubs are located in highly restrictive countries, and labour availability is severely affected by COVID-19 restrictions, experience larger market structure changes, for example, the manufacture of textiles (TEX), electrical equipment (EEQ) and coal (COA) sectors.
Although different sectors are heterogeneously affected by COVID-19 restrictions, we observe similar competition patterns among firms.According to Fisher's fundamental theorem (equation (2.11)), the change in a firm's market share is determined by the difference between its profitability and the average profitability of firms in the same sector (i.e. the variation in profitability).When a firm's profitability is lower than the average profitability in the sector (i.e. the variation in profitability is negative), it will lose market share to competitors (i.e. the production level  decreases).By contrast, when a firm's profitability is higher than the average profitability in the sector (i.e. the variation in profitability is positive), it will gain market share from competitors (i.e. the production level increases).Figure 5 presents the variation in profitability ( ξ ; see Methods) and the production adjustment ratio (κ; see Methods) of the five largest firms (i.e.countries) in the manufacture of electrical equipment, wholesale and retail trade, and education sectors under the explosive reopening scenario.A firm's production adjustment ratio represents its production level relative to the pre-pandemic level.Before full reopening, the variation in profitability of high-CHI (mid-and low-CHI) countries is almost consistently negative (positive).Therefore, we observe a decreasing (increasing) production level in these countries over the containment period.For sectors experiencing small market structure changes (e.g.wholesale and retail trade and education), the profitability of midand low-CHI countries fluctuates close to the average value, resulting in tiny increases in the production level in these countries.After full reopening, the profitability in high-CHI countries increases rapidly due to the recovery of labour capacity.However, the profitability is only slightly larger than the average value, resulting in a slight variation in profitability and a slow growth in the production capacity.The production level of some firms in high-CHI countries may not return to the pre-pandemic level even at the end of the projection horizon (figure 5j,k).These results indicate that high-CHI countries do not have significant advantages in profitability over midand low-CHI countries after full reopening.Although the global supply network may gradually resume to the pre-pandemic state after all restrictions are lifted, the moving process cannot be completed in 5 years.

Conclusion
To ramp up production after the pandemic, many firms have shifted supply chains away from countries where strict COVID-19 restrictions take place.In this study, we develop an evolutionary economic-epidemiological model to investigate how the difference in reopening pace across countries drives the evolution and reformation of the global supply network.Using real-world global air traffic data and the latest available global economic input-output data, our model characterizes the interplay between epidemic control and economic recovery across countries, and examines both short-term and long-term impacts of global reopening scenarios.
Our results suggest that, with a highly transmissible virus such as Omicron and the limited preventive effect of vaccinations, a widespread outbreak is inevitable after reopening, regardless of the timing and speed of reopening.Slower relaxation of strict policies leads to a limited reduction in the cumulative mortality rate at the end of the projection horizon.However, the limited public health benefits come at substantial economic costs, which include not only the short-term loss due to interrupted production but also the long-term loss due to supply-chain shifting.Restrictions on economic activities substantially hurt the profitability of firms in highly restrictive countries, making them less competitive on the global market and losing market share to firms in less restrictive countries.Although they can gradually gain back the lost market share after reopening, the business may not recover to the pre-pandemic levels within a short period of time because of limited advantages in profitability over competitors even after reopening.
With China's new 20 guidelines for easing the 'Zero COVID' policy, the world's manufacturing hub has lifted COVID-19 restrictions, which stimulates the vitality of the global supply network and economy.However, the decoupling of the USA and China casts a new shadow over the system with a potentially longer-lasting effect.The insights of this study are not limited to the COVID-19 pandemic but also other emerging infectious disease epidemics and geopolitical changes, such as the USA-China decoupling and the potential deglobalization worldwide.
Our research has limitations.First, due to the lack of firm-level data, interfirm supply-chain relationships were not incorporated into the proposed adaptive economic model.Thus, certain features of firm-level complexities in supply chains were missed [78,79].The collection of largescale, real-world firm-level data is essential to improve our understanding of supply-chain networks and their pandemic impact.Second, although the rule of 'growth of the fitter' embedded in this theorem is widely accepted in theoretical work [80,81], no empirical data are available to derive the actual rate of evolutionary change.However, sensitivity analysis shows that varying rates of evolutionary change do not affect our main results (electronic supplementary material, figures S14-S18).Third, although we use the adaptive policy adoption strategy to model the change in the stringency of NPIs, the upper and lower bounds of NPI stringency in each country (determined by the CHI score) are set according to simplified rules.Without a detailed roadmap to reopen in each country, it is difficult to model how the existing NPIs are lifted before full reopening.Our results can be updated and improved when more data becomes available.Fourth, due to the lack of real-world economic data under different reopening scenarios, we were not able to comprehensively validate the projected results in our model.However, some patterns identified by our study are consistent with the current shifting patterns in global supply chains observed in empirical studies.For example, we have shown that sectors such as the manufacture of electrical equipment will undergo larger market structure changes than sectors such as rice.These patterns have been shown in recent empirical studies, proving that the reallocation in global supply chains is evident for products such as electrical and electronic equipment [82], while food

Figure 1 .
Figure 1.Schematic illustration of the evolutionary economic-epidemiological model.The epidemiological model simulates disease transmission dynamics across countries based on the global mobility network.Using supply and demand constraints determined by the epidemiological model, the economic model projects the trade flows between firms in different countries based on the global supply network.

Figure 2 .
Figure 2. Public health impacts of different global reopening scenarios.(a) The CHI group by country/region on 1 March 2022 (t = 0).Countries/regions with CHI scores <25, ≥25 and <50 and ≥50 are defined as low-CHI, mid-CHI and high-CHI countries/regions, respectively.(b-i) Time series of the average prevalence (b-e) and cumulative mortality rate (f-i) in all (b,f ), high-CHI (e,g), mid-CHI (d,h) and low-CHI (e,i) countries/regions under different global reopening scenarios.Dotted, dashdotted and solid lines correspond to the results under the explosive, steady, and incremental reopening scenarios.Owing to the high prevalence rate in the first year, we only present the results from the second year of the projection horizon in the main text for clear illustration.Results for the whole projection horizon are presented in electronic supplementary material, figure S1.

' (u10 2 )Figure 4 .
Figure 4. Heterogeneous market structure changes in different sectors.a-c, Market structure changes ( M; see Methods) over the projection horizon by sectors under different global reopening scenarios.d-i, Each country/region's changes in market share relative to the pre-pandemic level by sectors at the end of the restriction period (d-f) and the projection horizon (g-i).Selected countries/regions have the largest national production before the pandemic.The left, middle and right panels correspond to the results under the explosive, steady and incremental reopening scenarios, respectively.Countries/regions and sectors are presented with three-letter codes.The description of the country/region and sector codes can be found in electronic supplementary material, tables S3-S4.

Figure 5 .
Figure 5. Changes in the global market under the explosive reopening scenario.The CHI score (a-c), the pre-pandemic market share (d-f ), and the variation in profitability (g-i) and the production adjustment ratio (j-l) of the five largest firms (i.e.countries) in the manufacture of electrical equipment (EEQ; the left column), wholesale and retail trade (TRD; the middle column), and education (EDU; the right column) sectors.a-c, Bars are coloured in red, orange, and green for high-CHI, mid-CHI and low-CHI countries/regions, respectively.The grey area and the solid grey line indicate the restriction period and the end of the restriction period.The grey dashed lines indicate the pre-pandemic levels.CHN, China; USA, United States; DEU, Germany; JPN, Japan; KOR, Korea, Republic of; GBR, United Kingdom.