Feedbacks between global supply chain disruption and the spread of SARS-CoV-2

The pandemic of COVID-19 has become one of the greatest threats to human health, causing severe disruptions in the global supply chain, and compromising health care delivery worldwide. Although government authorities sought to contain the spread of SARS-CoV-2, the virus that causes COVID-19, by restricting travel and in-person activities, failure to deploy time-sensitive strategies in ramping-up of critical resource production exacerbated the outbreak. Here, we analyze the interactive effects of supply chain disruption and infectious disease dynamics using coupled production and disease networks built on global data. We find that time-sensitive containment strategies could be created to balance objectives in pandemic control and economic losses, leading to a spatiotemporal separation of infection peaks that alleviate the societal impact of the disease. A lean resource allocation strategy is discovered that effectively counteracts the positive feedback between transmission and production such that stockpiles of health care resources may be manufactured and distributed to limit future shortage and disease. The study highlights the importance of cross-sectoral coordination and region-wise collaboration to optimally contain a pandemic while accounting for production.

sector are separated as a special sector to represent the expenditure on health care resources in human health and social work 33 . 87 The resources required by HHS are considered to correlate with the emergence of COVID-19 34 , reflecting the surge in demands 88 of critical medical supplies. Assuming each regional sector as a producer, the following information is obtained for each 89 regional sector: (1) the bill of material in production, (2) the pre-pandemic production capacity, and (3) the cross-regional 90 resource flow at equilibrium. 91 Figure 2. Global trade data analysis based on GTAP 10: a) Values of required raw material from different sectors to satisfy the doubled production of each sector. The rows of the table define sectors to provide the raw materials, and the columns of the table define sectors which double their production. b) Comparison of the production capacity, demands, and trade at the equilibrium between different regions. Here, the capacity is calculated by the total yearly production estimated from the total export and self-consumed resources. Demands are estimated based on the resource consumption from the household and government. Trade history is calculated based on resources exchanges in each region, including household, government, and companies. were to double. The increasing HHS production depends on inputs from many other sectors. The major inputs are from heavy Figure 3. Sectoral impacts of increased HHS capacity: a) Without coordinating other sectors, the regional shortage of resources after doubling the production of HHS in each region. b) Without coordinating other sectors, the averaged shortage of resource in five ramp-up scenarios, in terms of the pre-pandemic capacity (100), ramp-up by 25% (125), ramp-up by 50% (150), ramp-up by 75% (175) and , ramp-up by 100% (200). c) With coordinated supply chains, the averaged shortage of resource in five production ramp-up scenarios.
enables the control to weigh multi-objectives in the disease control and economic losses, thus finding a balanced solution. With 105 a higher capacity of producing HHS resources, the containment strategy tends to raise the HHS production to alleviate the 106 shortage of HHS resources so as to reduce the spread of the disease. Figure 3a shows the results of a stress test to identify the 107 vulnerable sectors in satisfying the demands from a health emergency. Results show that Grains and Crops is the least impacted 108 sector among all countries due to its weak dependence on other sectors. Transport and Communication is the bottleneck sector capacity function. With increasing production capacity, the shortage of HHS does not reduce monotonically, but fluctuates around 40%. As a result, significant shortages are observed in other sectors, including Mining and Extraction, Transport and 117 Communication, and Utilities and Construction, which overlap with dependent sectors in the Figure 2a. Other sectors, such as 118 Textiles and Clothing, suffer a remarkable shortage due to the shared input materials with the HHS resources, i.e., cloth and 119 masks. Increase in the production capacity is not enough to meet the surge in demands due to the limitations of raw materials.

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Without coordinated sectors, the ramp-up of production capacity incurs the overuse of materials in the existing stockpiles, 121 which leads to further raw material shortage in the future operation, thus deepening the disruptions in producing HHS resources.
122 Figure 3c shows the sectoral impacts when sectors are coordinated, namely, all the other sectors are able to provide sufficient 123 raw materials for HHS production. With increasing HHS production capacity, a clear decreasing trend of the HHS shortage is 124 observed, reducing from 60% shortage to less than 20% shortage. Note that even with sufficient production capacity, shortages 125 exist in Other Services and Utility and Construction, which require raw materials from the HHS resources for production. Figure 4. Disease impacts for increased HHS capacity. Assuming coordination of the supply chain is possible, the diagrams show the perentage of fatality reduction in different regions with the increasing production capacity of HHS resources, in terms of the pre-pandemic capacity (100), ramp-up by 25% (125), ramp-up by 50% (150), ramp-up by 75% (175) and , ramp-up by 100% (200). The fatalities simulated in the pre-pandemic capacities is used as a benchmark to calculate the reduction percentage. Figure 4 shows the influence of improved HHS production on the disease outcomes. As a benchmark, the number of dead 127 is calculated based on simulation results according to the pre-epidemic production capacity. The percentage of reduction 128 is calculated by comparing the total number of fatalities to the benchmark at each time instance. With coordinated supply 129 chains, an increase in HHS capacity at the early stage of the pandemic substantially reduces the number of fatalities as well as strategies: 1) pre-epidemic equilibrium (PE) strategy: adopt the pre-pandemic managerial decisions; 2) supply chain network 139 optimization (SCO) strategy: optimize the managerial decisions based on the demands and inventories; 3) coupled network 140 optimization (CNO) strategy: optimize the managerial decisions based on the interactions in the coupled networks. Figure 5   141 shows the effectiveness of these containment strategies in terms of infections in different regions.    Moreover, these containment strategies also ensure that at least one of the major HHS providers is available to support other 152 regions in each period of time, thus preventing an intense growth of the disease. 13.44%). As a comparison, the production disruptions for European Union and North America are reduced to 2.11% and 156 12.15% in May and 0.9% and 3.86% in June respectively in the CNO strategy (Fig. 6b). The better recovery of production to satisfy the surge in HHS demands under a health emergency, which highlights the need for inter-regional collaboration. America both lack the capacity to produce HHS resources, infections in Oceania are delayed, which reserves the production 165 capacity in health care resource preparation ahead of time to contain the disease growth. In contrast, low capacity and high 166 existing infections make Latin America rely on imports from other regions for disease control. The comparison shows that the 167 managerial decisions depend on regional production capacity as well as the connectivity to other regions.   The shortage of key equipment and materials during the COVID-19 pandemic and meeting the surging demands of 205 medical and personal protective equipment has been a significant challenge since the beginning of the pandemic. Researchers 206 acknowledge that ramping-up HHS resource production may not be as simple as raising the production capacity, but requires 207 the coordination of raw materials 9, 11 . In addition, the recent surge in HHS demands was found to stress supply chain networks to meet the demands to ramp-up HHS production, but also measured the minimal sector impacts with managerial decisions that 210 trade off the human cost and economic losses. Although these discoveries do not reflect all the underlying causes of supply 211 chain disruption, they significantly advance our ability to manage the situation by informing decision makers about vulnerable 212 sectors that have to be coordinated during an outbreak.

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Given the increased HHS production, enhanced inter-region collaborations at the start of the pandemic would have shortened 214 the pandemic period and reduced the threat to public health. In our model, containment strategies are customized by regions 215 according to their industrial structure and production capacity, thus leading to distinct roles of regions in a health emergency.

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Results highlight the need to strategically distribute the HHS stockpiles differently by region in order to prevent future resource 217 shortages. The active control model of the supply chain network tends to distribute resources to regions with major HHS 218 production capacity to prevent those regions from being disrupted by the lockdown policies caused by the pandemic, thus 219 improving the long-term HHS production supplies. to a substantial divergence in the long-term managerial strategies due to the feedback between the disease dyanmics and the 224 supply chain disruption. In the SCO strategy, ignoring the positive feedbacks makes the HHS export countries to overestimate 225 HHS demands thus being conservative in exporting, which in turn reduces the amount of HHS resources other regions receive.

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The increase in HHS shortages accelerate the disease growth, which in turns demands more HHS in the future, leading to a 227 butterfly effect 42 , where a small change in managerial decisions for a coupled nonlinear system can result in large differences in 228 outcomes.

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In summary, we proposed a coupled disease and supply chain network model using real-world data, and adopted existing 230 prevention policies. We quantitatively assessed the impacts of cross-sectoral coordination and agility in containing the outbreak. 231 We explored different containment strategies for critical medical supplies to seek the best managerial outcome in terms of

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Coupled supply chain and disease network. Each region is modeled as a patch with a disease model for simulating the 240 disease dynamics and a production-inventory model for production scheduling and planning. In particular, we use an SEIRHD 241 11/21 model of the disease with six compartments 43 , including susceptible (S) reflecting the part of the population that could be potentially subjected to the infection, exposed (E) representing the fraction of the population that has been infected but is not 243 infective yet, infected (I) representing the infective population after the latent period, hospitalized (H) representing the fraction 244 of infected individuals who need hospitalization, recovered (R) representing the population that has successfully cleared the 245 infection, and the fatalities due to the disease (D). The production and inventory model of region i is described by two states at 246 each time t: 1) inventory level of type k resource, V i,k (t); 2) backlogged demands for the type k resource, U i,k (t). We denote the 247 resource of type h as HHS resources. Thus, V i,h (t),U i,h (t) are the inventory level and demand for the HHS resources in region 248 i. Regional managerial decisions in region i, including production of type k resource, w i,k (t) and distribution to the public 249 o i,h (t), are the decisions to be optimized in the local inventory production planning. The resource production follows the bill of 250 materials M k ,k , which specifies the amount of type k resource required to product a type k resource.  Cross-region trade and supplies connect the regional inventories as a global production and supply chain network involving 257 region-wise trade decisions, i.e. o i ,i h (t) for importing resouces of type k from region i to i. Summarizing the above description, 258 we model the dynamics of the disease in region i using the following set of equations: where, N i is the size of population of region i. We note that γ IH = δ H /τ I ,γ IR = (1 − δ H )/τ I , γ HD = δ D /τ H , and γ HR = spreading on it, to describe the expected amount of production capacity available during the pandemic, namely whereW i,k is the pre-pandemic production capacity and γ w is a scaling parameter designed such that only 1% production 275 capacity remains available when the percentage of active infections reaches 1% of the total population.
where c h is zero when medical supplies are sufficient, and is 1 in the real-world scenario when the severe shortage of medical 299 supplies is experienced. All parameters are calculated directly from real-world data or from parameter fitting unless specified. terms, β i, j , i = j. To identify the best parameters for the coupled system, we fix the values of c i and d i to the levels identified in 320 the decoupled fitting, and search for the best transmission matrix G that fits the data. We define the transmission matrix G as where p i, j is a coefficient proportional to the number of daily travels from 322 region j to region i adjusted by the change in the international air travels reported by International Air Transport Association 323 (IATA) since starting the pandemic 48 , and ε is a fixed small number (ε 1) reflecting that cross-coupling has considerably 324 smaller effect on the disease transmission compared to the internal transmission. During each sub-interval, we seek for the best 325 β i and also the best ε that fit the worldwide COVID-19 data. It is observed that the suggested model and parameter estimation 326 approach fit the data with a reasonable accuracy. The trend of optimal tuning of the model parameters for each region is shown 327 in Fig. 7.  (1 + e 10 6 N i U i,h (t) ) 2 (23) The disease-dependent capacity function in Eq. (9) is also linearized to obtain With coupled dynamic systems there is no action that is exerted into the disease directly, but the changes in the supply chain propagate to the disease dynamics by affecting the remaining demands of HHS resources, U i,h (t) in Eqs. (14),(15),(18),(19).
The coupled network analysis enables managerial decisions aware of changes in both the disease dynamics and the supply chain as well as the opportunity to trade-off the objectives in disease growth and economic losses. The containment strategy is formulated by the following mathematical model, aiming to minimize the total fatalities, economic losses, and managerial cost where t p is the planning horizon, which is 14 days in this study, c u is the weight of the total economic losses compared to 336 the total fatalities in the planning horizon, c p,k and c l,k are the production cost and trade cost to obtain a resource of type k, 337 where c p,k < c l,k ,V i,k andW i,k specify the maximum production capacity and inventory capacity. Constraint (a) ensures that (c) ensures that production decisions of a certain area are always constrained by the available capacityW ; (d) ensures that 340 the inventory stocks are constrained by a regional inventory thresholdV . The model is solved by the Cplex package 49 . The