The energy rebound effect may weaken the impact of energy efficiency improvement on energy consumption. Therefore, the rebound effect is an important consideration in energy and environmental policies. This study takes the iron and steel industry as the research object, which is a large energy consumption sector in China, and the improved technique is used to estimate the energy rebound effect. The study constructs the dynamic energy efficiency utilizing provincial data from 2000 to 2019. The energy rebound effect from factor substitution and output expansion is then calculated. The research further discusses regional differences in the energy rebound effect. The results indicate that the technical progress of the iron and steel industry promotes energy efficiency improvements. The eastern region shows the best energy efficiency performance, followed by the central area, and the western region performs the worst in energy efficiency. The industrial energy rebound effect is 0.4297, which partially offsets the energy reduction caused by energy efficiency improvements. Factor substitution and output growth produce the industrial energy rebound effect. Furthermore, the rebound effect exhibits distinct geographical features. The policy suggestions are finally proposed to mitigate the industrial rebound effect and achieve energy and carbon reductions. This contradiction also intensifies energy constraints on the economy’s sustainable development. In the new century, global energy consumption increased rapidly. According to the International Energy Agency, global energy consumption in the year 2019 was 606,490 PJ  forms a complete production system, and its industrial output ranks first in the world. eduction . The Cen2 reduction contributes to green industrial development. The benefits of green production in the ISI can be summarized in two aspects. On the one hand, there is currently a risk of the oversupply of steel products in China. Green development is a key driving force for the transformation and upgrading of the ISI. The green transformation of firms can eliminate outdated capacity and promote China to become a high-quality iron and steel producer. On the other hand, green development requires reducing energy intensity and improving energy structure. It is an important step to address the environmental pollution problem caused by iron and steel production at the source. For these two reasons, the energy and environmentally friendly development of this industry attract stakeholders’ attention. In September 2019, fifteen large Chinese steel firms jointly issued the Declaration on the Green Development of Chinese Steel Enterprises. This practice shows that by taking initiatives in green production, iron and steel firms can achieve harmony with the natural society.The effectiveness of energy conservation and COImproving energy efficiency is considered a cost-effective tool to achieve energy and ecological-friendly targets ,15. UndeCurrently, policies are often formulated focusing on the technical aspects of the potential for energy savings, ignoring the linkages between a firms’ production behaviors and the socioeconomic system. As a result, the prospect of energy conservation is often overestimated, and energy-saving and environmental-friendly policies are not working. Reliably quantifying the rebound effect is essential to estimate the actual energy savings resulting from energy efficiency policies. To present a practical plan to minimize energy usage, this research measures the energy rebound effect of the ISI from the producer’s perspective. The study aims to answer three questions concerning the ISI. (1) What is the present state of industrial energy efficiency? What are the features of energy efficiency performance and influence factors in different regions? (2) Is there an energy rebound effect in the context of energy efficiency, and what is the influence mechanism? In particular, how do factor substitution and output growth contribute to the rebound effect? (3) Does the energy rebound present heterogeneously in different regions of China, where economic and industrial development patterns range greatly? The quantitative investigation of the energy rebound effect aids in explaining energy use in the ISI.The innovation of this article includes three layers. (1) Most earlier research estimates energy price elasticity as the rebound effect because of limited data on energy efficiency and energy services. However, if the energy price is strictly regulated, the variation range may be negligible. The use of energy price elasticity estimates may be biased. Drawing on the improved method of Liu et al. , this stThe study’s following chapters are structured as follows. The Jevons’ Paradox is the earliest study of the rebound effect, which is one of the most important topics in energy economics. In other words, improving fuel  efficiency tends to increase (rather than decrease) fuel use . HoweverIn the new century, the major problem of energy security prompts people to explore energy-saving means actively. Under such a background, the rebound effect received greater attention. Berkhout et al.  intuitivThe existing studies provide a rich methodological basis for exploring the rebound effect. In summary, there are three main approaches, which include the quasi-experimental method, computable general equilibrium (CGE), and the econometric model.The quasi-experimental method measures the energy services demand changes before and after the energy efficiency improvement. However, this approach does not use control groups or control confounding variables and cannot control for other factors that may impact energy services demand . Due to It is also common to apply the CGE model to the macroeconomic level in the literature ,38. BrobMore researchers develop econometric models nowadays to carry out their research. Econometric approaches allow for a more precise estimate with the use of production functions. These techniques can also be altered in accordance with certain theoretical presumptions. In addition, these methods can be modified according to different theoretical assumptions. It is important to note that the setting of the specific production function form may affect the results . Yang anThe rebound effect is widely acknowledged in the academic world, although its significance is frequently debated. The academic discussion over the rebound effect focuses mostly on its causes and magnitude. The literature thoroughly investigates its effect magnitude and mechanism from many angles. Scholars of the neoclassical growth theory explain the formation mechanism of the rebound effect from the viewpoint of consumer and producer theory. Some studies from the consumer side focus on household sectors, such as in ,48. But For China’s ISI, the existing research focuses on energy consumption and energy efficiency . H1. The energy rebound effect exists in the ISI, and energy efficiency improvement can not fully achieve energy conservation goals.H2. The impact of factor substitution on the rebound effect is greater than that of output expansion.H3. The rebound effect shows up differently in different regions.This study draws on the idea of a two-stage estimation approach . The firIn the first stage, we construct a dynamic energy efficiency indicator, namely the Malmquist energy performance index. Caves et al.  first deUsing the DEA model, the production technology can be written as:This study requires that the energy input be reduced as much as possible within the production possibility set, while keeping other inputs and outputs constant. Following the study of , this stThe above equation indicates the energy productivity change between τ and τ + 1, which can be divided into the following two parts.The efficiency index is a dynamic energy efficiency that considers energy use efficiency and technology changes; chnology .Following the study of ,66, the The measurement of the rebound effect is vital for this paper, as it is the basis for determining whether and to what extent a rebound effect occurs in the industry. Critical to iron and steel production are energy services. Therefore, we take energy services, capital, and labor as inputs to the production process and construct the translog cost function in the second stage . The traUsing Shephard’s Lemma, this study finds the partial derivative of the logarithm of the factor prices. The cost share equation is described as:The observed cost shares in practice are affected by the perturbation term. Therefore, the observed cost share equations can be constructed as:Substituting According to , the parIn this study, the equations’ parameters are estimated using the seemingly uncorrelated regression method . This meAfter estimating the parameters in Equation (9), we focus on the response of producers to changes in input prices. The Allen–Uzawa elasticity of substitution (AES) and cross-price elasticity (CPE) are standard measures of response to price changes . The AESIf Based on the study of , the dirThe direct rebound effect through the output channel (The energy rebound effect (RE) can be composed of two parts: one is the factor substitution effect, and the other is the output effect . TherefoThis study selects provincial data to calculate energy efficiency and the energy rebound effect of China’s ISI. Considering data availability and data statistics consistency, we chose 2000–2019 as the sample period . Due to The variables used to explore the industrial rebound effect are described as follows.(1) Industrial output (Y) and its price (PY). Measures of industrial output include the industrial products, industrial value added, and gross output. Due to the variety of products, the gross output value data are taken as the desired output. The data between 2000 and 2016 is from the China Industry Statistical Yearbook, while the data between 2017 and 2019 is from the Statistical Yearbook of each province. It is because after 2016, the China Industry Statistical Yearbook no longer covers gross output data. This study deflates the raw data using the ex-factory industrial price index and converts it to the industrial output value at the constant price in 2000. Its price is expressed by the producer price indices for industrial products. The data are obtained from the China Statistical Yearbook.(2) Labor (L) and its price (PL). Labor input is measured by the average employment population in the ISI. The labor data comes from the China Industry Statistical Yearbook. The labor statistics of individual years are missing, so we use the linear difference method to fill in. This study uses the average wage of employees as the industry’s labor price, and then deflates it by using the consumer price index to obtain the real labor price in constant with the year 2000 prices. The wage data are from the Labor Statistical Yearbook and the consumer price index is from the China Statistical Yearbook.(3) Capital (K) and its price (PK). Capital stock is used to measure the capital input. No official statistics on capital stock are published in China. The common method currently used in the academic community is the perpetual inventory method proposed by . We empled to in ,75. The ed to in , and the(4) Energy use (E) and its price (PE). The energy consumption of the industry can be used as an energy input. Based on the energy conversion factors, we convert different kinds of energy into standard coal, and then aggregate them to get the total energy use of the ISI. Data for each energy use are obtained from the Statistical Yearbook of each province and data for conversion factors comes from the China Energy Statistical Yearbook. For some provinces without energy data reports, we draw on the studies of ,77 for eIn terms of regions, the eastern region shows the best efficiency performance at 1.106, higher than the national average. It is driven by an improved energy use efficiency and technical progress in the eastern area. This region has the advantage of an obvious catch-up effect and frontier-shift in steel production. This finding is in line with reality . With a The Five-Year Plan is an important part of China’s national economic plan. The goals put forward by it have a great influence on economic departments. Comparing energy efficiency differences in each period can provide further insight into the energy management of the ISI. Referring to the method of , we calcAfter obtaining the energy efficiency, we can calculate the effective energy service and substitute it into the production function as an input factor. This study uses seemingly uncorrelated regression to the equations for the labor and effective energy service. The estimated results of the parameters are reported in We further calculate the price elasticity of each input factor, which is presented in The energy rebound effect is caused by energy services allocation due to changes in the relative price under technical progress. To understand the mechanism of the rebound effect more intuitively, The industry’s average nationwide rebound effect is 0.4297, showing a partial rebound effect and verifying the H1. The potential energy conservation is realized at 57.03%, which indicates a large space for energy savings. The reason for this is that energy efficiency leads to a reduction in energy services prices. Under the imperfect energy price system, it is inevitably difficult to curb energy consumption to meet the increasing production demand. The additional energy services input is stimulated under the effect of factor substitution and output expansion. The rebound effect from the substitution channel is 0.3279, and from the output channel is 0.1018. It is clear that the substitution channel is more significant than that output channel (H2 is verified). The rebound effect of the ISI is mainly driven by factor substitution, while output expansion plays a relatively minor role. Lower energy services prices incentivize iron and steel firms to engage in factor substitution . The smaChina is a vast country with significant economic differences across its regions. Analyzing the rebound effect from the whole country may overlook the heterogeneity of regional development. Therefore, we further explore the rebound effect of the ISI in each province. China’s ISI is the industrial sector with a very high energy consumption and pollutant emission. With environmental deterioration and energy shortage constraints, this industry is facing a severe situation. How to achieve high-quality development while reducing energy consumption has become a major problem to be solved urgently by the government and industry. At present, the energy conservation policy of the ISI is mainly implemented by administrative controls. Although this approach may produce energy-saving effects in the short term, the economic and social costs are relatively high. In this case, firms lack incentives for long-term energy efficiency improvement. The existence of the rebound effect highlights the importance of a market-oriented approach . The theEnergy efficiency is an essential means of energy saving and environmental protection. However, the energy efficiency will bring about a rebound effect. This article explores the energy rebound effect of the ISI with the improved method proposed by . The stu(1) The dynamic energy efficiency of the ISI is 1.08. Its improvement is driven by energy technology progress. The best energy efficiency performance in eastern China is driven by the combination of energy use efficiency improvement and energy technology progress. The central region has the second-best energy efficiency performance while the western region has the lowest energy use efficiency, resulting in their energy efficiency performance lagging behind other areas. The green transformation of the ISI needs to pay attention to improving energy efficiency. It requires great effort in energy utilization and energy technology. On the one hand, efficient energy utilization can be realized by adopting modern production management. On the other hand, firms can strengthen the invention and promotion of new metallurgical technology in production.(2) The energy rebound effect does exist in iron and steel production. It means that energy efficiency improvements do not bring about the expected energy use reduction. The average rebound effect is 0.4297, showing a partial rebound effect. Potential energy savings from improved energy efficiency reached 57.03%. Although energy efficiency improvements lead to the rebound effect, the energy backfire does not occur. It indicates that in most cases, the amount of energy saved by efficiency improvement is greater than the amount of energy rebound. Thus, improving energy efficiency remains an effective way to save industrial energy use. As for the decomposition, factor substitution is more critical in promoting the rebound effect, with a value of 0.3279, and the impact of an output increase on the rebound effect is 0.1018. This finding highlights the role of the rebound effect in the green economy of the ISI. Ignoring the rebound effect will greatly diminish the effectiveness of green transition policies and actions. A market-oriented reform of production factors, especially energy prices, will help promote high-quality development of the ISI.(3) In terms of provincial distribution, the rebound effect shows regional heterogeneity. It is relatively concentrated in the central provinces. The reason is that the central provinces have better resource endowments and the convenience of accepting industrial transfer. The rebound effect of the western region is the lowest, which is related to the small scale of steel production and the lagging technology in this region. Economic development, resource endowment, and industrial policy are the critical factors leading to regional differences. This reveals that the high-quality and green development of the ISI needs to optimize the regional layout. Market demand, resource guarantee, and environmental capacity are key factors for firms to consider in the future.This paper explores the energy efficiency and rebound effect of China’s ISI. According to the conclusion, we put forward suggestions to address the energy conservation and environmental protection challenges.First, it is urgent to enhance industrial energy efficiency through technological advances. The energy savings are the result of the combined effect of the theoretical energy saving and the rebound amount brought by energy efficiency. Technical innovation is responsible for current production efficiency and energy consumption. Therefore, iron and steel firms need to improve their independent innovation capability in the low-carbon economy. Firms should strengthen investment in energy-saving production technology research and development. Firms can further update advanced technology equipment and eliminate high energy-consuming obsolete equipment to improve energy efficiency. In addition, firms should pay attention to management innovation, system optimization, and other soft technological advances for effective resource allocation. This is because it can better raise awareness of energy conservation and promote energy efficiency improvements by managing the optimal use of energy elements. For the country, the government should watch out for the technology spillover effect between regions and technology transfer ,84. The Second, the government should improve the policies’ effectiveness and focus on energy prices in the ISI. This study finds a high rebound effect in the ISI. Governments and firms need to become aware of the rebound effect gradually. The rebound effect affects how energy efficiency improvements reduce energy consumption . It alsoThird, the ISI should consider regional differences in developing energy efficiency policies. The rebound effect in the ISI is regionally heterogeneous, and improving energy efficiency generates different levels of demand for energy services. Differentiated energy conservation policies should be formulated in the context of regional development. High energy-consuming equipment should be restricted in the central region with a rich resource endowment. Meanwhile, the central area should change the energy structure dominated by coal consumption and strengthen clean energy utilization. The additional energy consumption will be added, provided the rebound effect exists. The problems of resource depletion and environmental pollution are expected to be ameliorated if the energy mix is rationalized so that non-fossil energy sources are the main component of the increased energy consumption. Iron and steel firms can establish a clean production system and introduce more renewable energy generation through energy storage . As the This research provides a useful reference for future research on the energy rebound effect of China’s industrial sectors. At the end of the article, we need to point out that there may be some flaws and limitations in the study. First, coal energy and capital prices are regulated by the Chinese government and not fully determined by the market. Limited by data availability, this study cannot obtain data on the energy and capital prices of the ISI. We apply the provincial fuel and power purchase price index and capital price as the proxy. These data may affect the result of energy efficiency and the rebound effect. Second, the estimation of energy efficiency is the basis for the rebound effect. There are other alternative methods, such as the stochastic frontier approach, that can estimate energy efficiency. Moreover, the selection of different production functions and input factors may also affect the rebound effect estimation. These questions need to be considered in future research. With the deepening of market-oriented reform, more comprehensive data will provide new support for the research. Additionally, with new methods, the industrial rebound effect estimation will be more accurate and closer to the actual situation. In future studies, calculating the rebound effect of different energy types in the ISI may yield more findings.


Lateral driving behavior analysis is the foundation of freeway cross-section design and the focus of road safety research. However, the factors that influence vehicle lateral driving behavior have not been clearly explained. The dataset of the natural driving trajectory of freeways is used in this study to analyze vehicle lateral driving behavior and trajectory characteristics. As vehicle trajectory characteristic indicators, parameters such as preferred trajectory deviation and standard deviation are extracted. The effects of lane position, speed, road safety facilities, and vehicle types on freeway trajectory behavior are investigated. The results show that lane width and lane position significantly impact vehicle trajectory distribution. As driving speed increases, the lateral distance between vehicles in the inner lane and the guardrail tends to increase. In contrast, vehicles in the outside lane will stay away from the road edge line, and vehicles in the middle lane will stay away from the right lane dividing line when the speed increases. Statistical analysis shows that the preferred trajectory distribution of the same vehicle type in different lane positions is significantly different among groups (Cohen’s d > 0.7). In the same lane, the lateral position characteristics of the center of mass of different vehicle types are basically the same (Cohen’s d < 0.35). This work aims to explain what variables cause trajectory deviation behaviors and how to design traffic safety facilities (guardrail and shoulder) and lane width to accommodate various vehicle types and design speeds. Recent years have seen an increase in light-duty vehicles, represented by passenger cars, vans, SUVs, and pickup trucks. Many cities in China have begun to build light freeways , such as Shenzhen’s Jihe freeway and Fujian’s Quanxia freeway. This measure has proven to be an effective way to take into account traffic safety, comfort, and resource conservation. It can prevent the reduction in road capacity and serious traffic conflicts caused by traditional mixed traffic. Lane width, as a critical indicator of light freeway cross-section design, not only meets the safety needs of vehicle overtaking and moving side by side, but also meets the psychological safety distance required by drivers from the road environment. As a result, on the one hand, a thorough understanding of the lateral driving behavior, lateral position preference, and influencing factors of vehicle trajectories can assist some cities in designing and building light freeways by providing data support and specification preparation basis. On the other hand, it can reveal the mechanism of freeway traffic accidents, which is useful for researching freeways accident prevention strategies.Previous research has primarily focused on the impact of lane width on traffic flow characteristics. Peng et al.  proposedFor nearly two decades now, statistical methods have been used to investigate the impact of road cross-sectional parameters on driving safety or to develop accident prediction models . Wood etIn summary, most previous studies focused on single-factor correlation analysis, and the majority of the data collected were cross-sectional observation data, accident data, driving simulator collection data, and computer simulation data in regular roads, which ignored the fact that the natural running of vehicles was a continuous process and could not reveal the influence mechanism of real road environment, lane position, and vehicle types on driving behavior, which would affect the research’s accuracy. It cannot provide reliable evidence for the cross-section design and revision of standards and specifications of special freeways for cars without the verification of massive vehicle trajectory data, and the risk assessment method by using accident data cannot reveal the mechanism of traffic safety accidents on freeways.In this paper, the preferred trajectory deviation is proposed for the first time to characterize lateral driving behavior using the natural driving trajectory dataset of German freeways. The trajectory behavior analysis in a wider and higher speed range is carried out in the straight section of freeway. This work aims to investigate how lane position, vehicle type, and vehicle speed affect trajectory deviation. It distinguishes the differences in center of mass between cars and trucks. Clarification of vehicle trajectory behavior characteristics and influencing factors can provide a valuable theoretical basis for determining key technical indicators of freeway cross-section and road safety facilities such as guardrail and shoulder, thereby reducing the drivers’ psychological load.The HighD Dataset, a drone dataset of naturalistic vehicle trajectories on German freeways, is used as the data source for freeway vehicle lateral position analysis in this paper . The recThe HighD dataset was recorded on straight freeway sections in six different locations near Cologne, Germany. There were two or three lanes in each direction. The shooting range on the straight sections is approximately 420 m. Because some German freeways have no speed limits, the trajectory data of a wider speed range can be observed, and analysis of its trajectory behavior characteristics can provide key indicators for the cross-section of freeways at different design speeds. Lane keeping is among the most common events on the freeway. The natural driving behavior of vehicles in straight sections is observed, It is discovered that drivers will not strictly keep the center of the vehicle in the lane centerline, but use the lane width to keep the vehicle in the lane. In other words, the vehicle trajectory point deviates from the lane centerline and swings. Therefore, this paper proposes the preferred trajectory, the preferred trajectory deviation, and the preferred trajectory standard deviation index to describe the lane vehicle’s trajectory behavior characteristics. The parameter calculation is shown in i in ascending order. Lane markings run horizontally in the image. Therefore, their positions can be indicated by a y-coordinate, where left,iy is the longitudinal coordinate of lane i’s left lane marking; mid,iy is is the longitudinal coordinate of lane i’s centerline; and right,iy is the longitudinal coordinate of lane i’s right lane marking in the coordinate system. The vehicle trajectory is excluded if it is not recorded by the aerial video throughout the process. Then, the trajectories with the number of lane changes of 0 will be taken as the object. The coordinates of the trajectory point  and the coordinates of the road marking are superimposed in the same coordinate system to obtain the trajectory-road marking topology relationship. The average value of the longitudinal coordinates of the trajectory point is the preferred trajectory, and the formula for calculating the preferred trajectory is shown in Equation (1). The distance between the preferred trajectory and the centerline of the lane is the preferred trajectory deviation, and the formula for calculating the preferred trajectory deviation is shown in Equation (2).n is the number of trajectory points; ny is the longitudinal coordinate of the vehicle’s the nth trajectory point; preferredy is the preferred trajectory, representing the driver’s lateral preference position in the lane; dl is the preferred trajectory deviation. When the preferred trajectory falls on the left of the centerline of the lane, the preferred trajectory deviation is negative. Otherwise it is positive. In this study, the 15th and 85th percentile of the preferred trajectory are used as the feature numbers to show the drivers’ lane utilization.The preferred trajectory characteristic parameters of the concrete calculation method are shown in Driving behavior in the lane is the result of psychological load, environmental perception, and road geometric characteristics. The preferred trajectory represents the driver’s preferred position in different lane environments and speeds. It can aid in understanding the mechanism of driving behavior as well as the impact of multiple factors on driver trajectory selection behavior.The preferred trajectory deviations of the six-lane divided freeways are depicted in The dispersion of the outside lane of the six-lane divided freeway road (3.75 m) is greater than that of the inner and middle lanes (3.5 m). The dispersion degree of the middle lane is smaller than that of the inner lane, indicating that the wider the lane, the more lateral space is provided for vehicles, and the dispersion degree of the trajectory will also increase. Moving vehicles are on both sides of the driver in the middle lane. To avoid collisions with parallel vehicles traveling in the same direction, a clear lateral distance will be maintained with both sides, and the preferred trajectory will be limited, resulting in a lower dispersion degree than that of the same width lane. Furthermore, when traveling in parallel with trucks, drivers perceive greater safety risks than small cars, resulting in a greater lateral distance between them. As a result, the lane width, and the environment (including the types of neighboring vehicles and roadside facilities) on both sides of the lane influence vehicle lateral driving behavior.To investigate the influence on vehicle preferred trajectory deviation in different scenarios, the preferred trajectory distributions of the inner and outside lanes of the four-lane divided freeway and six-lane divided freeway were compared and analyzed to investigate the differences in lateral driving behavior of the same lane location in different scenarios, as well as to compare the breakdown of the major vehicle types in the lanes.As shown in y = 0 is located represents the centerline of the lane. The preferred trajectory deviation is positive when dl falls on the right side of the centerline of the lane. Otherwise, it is negative.To determine the critical index values of cross-section facilities required by light freeways at different design speeds, it is necessary to explore the trajectory control characteristics of car drivers at different speeds. This section selects the preferred trajectory deviation of passenger cars at different speeds for comparison. This section compares the preferred trajectory deviation of cars at various speeds. The neighborhood of 10 times in the range of 100–160 km/h is chosen as the speed retrieval condition, and the neighborhood’s floating threshold is −3–3 km/h. The sample size is approximately 300 vehicles under different speeds. The change in trajectory control behavior after speed increase can be explained by the “field of safety” theory. Gibson et al.  suggest As the vehicle’s speed increases, so does its original field force, and the energy and harm caused by collision with the guardrail is greater, so the vehicles in inner lane will tend to stay away from the median guardrail. The virtual “external force” generated by the vehicle in the outside lane, particularly the truck, increases, forcing the vehicle in the middle lane to change its motion state during acceleration and move laterally to the left to obtain more safe lateral space. Furthermore, the potential field strength (constraint effect) of the road boundary field is increased, and vehicles in the outside lane are more willing to continue driving in the center of the lane. As a result of the increased speed, vehicles in the inner lane tend to be further away from the guardrail, and the lane should be adjusted to the outer side (right side). Namely, after increasing the design speed, the width of the left marginal strip should be increased moderately.To clarify the differences between the operating characteristics of light-duty vehicles and large trucks, and to derive the key indicators of freeway suitable for light-duty vehicles, the motion behavior of both must be analyzed. To ensure that lane position and roadside environmental variables do not affect vehicle trajectory characteristics, the objects for comparative analysis are the mixed passenger and freight lane in two cross-sectional forms. p value of the test result is less than 0.05, the statistical result is significant, indicating that there is a significant difference between them. Cohen’s d is the effect size that indicates the difference between groups. The values 0.20, 0.50, and 0.80 correspond to small, medium, and large effect critical points.The T-distribution theory is used to infer the probability of difference, so as to compare whether there are significant differences between the two data groups. Statistical method of paired T distribution is calculated, the differences in trajectory control between different vehicle types in the same lane and the same type in different lanes are compared, and the significance of vehicle types and lane width is analyzed. Among them, when the eigenvalues of preferred trajectory distribution was selected from 10th to 90th, and the actual lane width occupied by different types in this distribution range was calculated. For straight road sections with lane widths of 3.5 and 3.75 m, the usage lane widths of trucks are 3.3 and 3.6 m, and the usage lane widths of cars are 2.5 and 2.8 m.Statistical analysis in There are significant differences when comparing the same vehicle type’s preferred trajectory deviation distribution in the outside lane (3.75 m) and the middle lane (3.5 m). The difference between trucks in different lane is medium, and the difference between cars in different lane is large. This demonstrates that changes in the roadside environment and lane width result in different trajectory behavior characteristics of the same type of vehicle, and car drivers are more sensitive to perception and response to the surrounding environment.This research differs from previous single-factor research in that it considers many key factors of the “human-vehicle-road” collaborative safety system. The data source employed is large-scale driving trajectory data, which is more accurate than data collected by driving simulation technology. The research findings are more credible when applied to engineering design. According to current research , the preMeanwhile, this study found some interesting conclusions that were not found in previous studies:When the vehicle’s speed increases, so do the virtual external forces that act on it. Guardrails, parallel vehicles, and road markings can provide virtual forces, and the force increases with speed. This aids in understanding the mechanism of driving behavior and its relationship to speed and road facilities, as well as providing a theoretical foundation for geometric layout and road safety protection measures at higher design speeds. For example, setting a wider distance between the inner lane and guardrail when design speed is improved. Additionally, increasing the width of the middle lane contributes to a better sense of security.However, we must add a word of caution. The differences in driving styles cannot be ignored and should be investigated further. Further, other common road geometric features that need to be considered include circular curves with various radii and slopes. Another limitation could be the lack of bridge or tunnel scenes in the dataset. To strengthen the findings, future research should look into potential differences in driving styles, individual characteristics, geometric alignment, and traffic facilities.(1)The preferred trajectory deviation is affected by lane position and the roadside environment. The preferred trajectory of the vehicle tends to be close to the roadway edge line when there is a shoulder or marginal strip on the outside of the lane; the middle lane tends to stay away from the trucks.(2)By narrowing the lane, the preferred trajectory’s dispersion can be limited. Furthermore, lane position and roadside facilities influence the preferred trajectory dispersion, and the vehicle trajectory dispersion in the middle lane is lower than in the other two lanes.(3)As speed increases, the distance between vehicles in the inner lane and the guardrail increases, and the vehicle preferred trajectory in the middle lane continues to move to the side away from the truck, while vehicles driving in the outside lane tend to close the lane’s centerline; thus, as the design speed increases, the width of the marginal strip should be appropriately increased to meet the demand of drivers’ psychological safety.(4)The preferred trajectory deviation of the same type of vehicle in different lanes is noticeably and significantly different. Car drivers are more sensitive to their surroundings’ perception and reaction than truck drivers.(5)According to statistical analysis, lane position and roadside environment are significant factors influencing the vehicle preferred trajectory deviation. When different types of vehicles are mixed in the same lane, the difference between the center positions of cars and trucks is small; in other words, the lateral position characteristics of the center of mass of cars are essentially the same as those of trucks, which can be used to justify lane width reductions on light freeways.This study analyzed the influences of lane width, lane position, road facilities, vehicle types, and speed on lateral driving behavior and trajectory control characteristics by using open natural driving trajectory dataset. The main findings can be summarized as follows:


There has been a rapid increase in the use of collaborative robots in manufacturing industries within the context of Industry 4.0 and smart factories. The existing human–robot interactions, simulations, and robot programming methods do not fit into these fast-paced technological advances as they are time-consuming, require engineering expertise, waste a lot of time in programming and the interaction is not trivial for non-expert operators. To tackle these challenges, we propose a digital twin (DT) approach for human–robot interactions (HRIs) in hybrid teams in this paper. We achieved this using Industry 4.0 enabling technologies, such as mixed reality, the Internet of Things, collaborative robots, and artificial intelligence. We present a use case scenario of the proposed method using Microsoft Hololens 2 and KUKA IIWA collaborative robot. The obtained results indicated that it is possible to achieve efficient human–robot interactions using these advanced technologies, even with operators who have not been trained in programming. The proposed method has further benefits, such as real-time simulation in natural environments and flexible system integration to incorporate new devices . Traditional production systems face a variety of difficulties, such as high demand for customized products, just-in-time production, shorter product life cycles, small batch sizes, etc. . Such chWith the onset of Industry 4.0, manufacturing industries have increasing access to various technology drivers, such as big data and analytics, the Industrial Internet of Things (IIOT), cyber–physical systems (CPSs), cloud computing, additive manufacturing and augmented, virtual and mixed realities (AR/VR/MR), among others . More rePowerful and intuitive interfaces are needed to achieve secure and able digital twin-guided HRIs . AdditioA diverse range of industrial applications requires the simulation of planned motions. This enables the avoidance of defects and collisions and the optimization of planned tasks before they are executed by real robots.This work envisioned the future of robot programming and robot simulation within an industrial environment in which humans and robots work side by side. The main objective of this work was to build and demonstrate a new digital twin-based framework that was designed to enhance human–robot interactions, robot programming and real-time simulation in real environments. The proposed approach would be required to create a flexible real-time service-based framework for both vertical and horizontal integration. It would also be needed to provide an intuitive and human-friendly usage for unskilled workers. A horizontal technological architecture based on the Internet of Things, mixed reality, artificial intelligence and system integration was used during the implementation of different steps.A novel digital twin for a human–robot interaction framework using Industry 4.0 enabling technologies;A use case study of the use of the proposed framework with an industrial robot in real-time.The following contributions are made in this paper:The rest of the paper is organized as follows. Interactions between human beings and robots have changed considerably throughout history. They started with simple physical interactions using basic tools, such as a mouse or a keyboard, following which they developed to the use of touch screens as interactive interfaces. Over the past few years, robots have started to easily interact with human partners via gestures or voice, thanks to their growing autonomy and the introduction of new software and hardware capabilities . GradualTo program collaborative robots (robots that are intended for direct human–robot interactions within a shared space) for the previously mentioned types of interaction, different programming approaches exist. We can mainly organize them into two categories: online and offline programming . Online Teach pendant programming involves a hand-held device, which is generally attached to a robot and used to teach the robot specific points, locations and path sequences. This technique is suited for applications that have a point-to-point control and for which only one controller is sufficient to determine the trajectory of the robot. However, this method has several limitations: (1) it is difficult to achieve high accuracy for several geometrical trajectories; (2) it is difficult to connect to external devices; and (3) it interrupts production lines when a new task is programmed [ogrammed .Lead through programming, also known as programming by demonstration (PbD), aims to enable robots learn new skills from human guidance. It helps non-experts to teach robots without any previous programming knowledge as this method just needs the operator to guide the robot manually into the desired position and record the path [the path . HoweverOffline robot programming helps to resolve the limitations of online methods. It generally involves a dedicated programming and simulation software that aims to design and plan robot movements. Commonly, it is the remote simulation of a 3D graphical model of the work cell environment [ironment .This method ensures that planned control algorithms can be implemented correctly before their execution on a real robot . It alsoVR-based robot programming is an offline programming method in which the system guarantees secure and offhand virtual programming [gramming . The traAR-based robot programming provides excellent opportunities for HRIs and has been widely explored for use in telerobotics. It allows the worker to operate as though the worker were in the remote working environment [ironment . Its potironment , in whicIn , Fang etA digital twin is a digital replica of a real-world physical system, which aims to enhance the accuracy of simulation capabilities . This coThe DT aspect allows for real-time optimization and decision-making interventions, based on the simulation of a virtual model in the real world. This technology should not be confused with the notion of the Internet of Things (IoT). For the IoT, we collect data from a physical object and its environment through sensors, while for DTs, data are injected into the virtual objects. Other emerging technologies, such as AR, HMI dashboards and AI, are also needed to enhance physical connectivity and real-time machine outcomes .Many researchers have investigated the topic of DTs within the context of Industry 4.0 and, more specifically, for human–robot interactions ,35. A DTTraditional robot programming methods require highly paid and qualified engineers and a lot of time (online);Unskilled workers cannot program robots easily (text-based offline);It is not possible to teach complex collaborative tasks using online robot programming;Operators cannot preview movement simulation in real time or in a real environment using offline or VR-based methods;Traditional robot programming and simulations do not fit in smart factory environments (text-based offline);Human–robot interactions in hybrid teams need to be more efficient and human-friendly;The integration of new robots or devices impacts the whole system, which then requires reconfiguration (text-based offline).From the previously cited methods : This consists of the communication establishment layer. It aims to maintain the interconnection bridge between the real world  and the virtual world. This layer enables the exchange of data inside our system. It is important to notice that at this level, both the real and digital worlds should be set up and ready to use, including:Machines, devices and sensors that are ready to send and receive data via one of the IoT standard messaging protocols ;Digital content, which includes the digital twins of some of the real components and additional computer-generated data, that is developed, visualized and ready to communicate data.Since the digital environment is represented in a 3D holographic immersive shape, MR technology is used in the Connect step that enables the visualization and interactions with the digital content. The Connect step is primordial and must always be the first to be initiated before starting any other operation using the DT-HRI system. So, Connect is mainly based on the IIoT, as well as MR technologies.Step Two (“Collect”): After enabling the Connect step in the different elements of the system, data then need to be collected and transformed into information to synchronize both scenes for the initial start-up of the process. The Collect step is performed using an IoT gateway communication pattern.Step Three (“Combine”): After connecting the real and digital environments and collecting the data from each part, the Combine step merges both worlds to look as though they are one single environment. In the HRI context, the Combine step has two major goals: (1) the superimposition of the digital twin onto the real-world model, which means that the digital model overlays onto the same position as the physical model; (2) the digital model having the same initial configuration as the physical model. The visualization of holograms in the real environment and interactions with them require MR capabilities. As a result, the Combine step is based on MR technology.Step Four (“Process”): After setting up all of the environmental components, communication and data collection and the combination of both worlds into one environment, the system is ready to operate. The Process step is for the analytical and processing brain of the system, as the name indicates. At this level, data processing and algorithm generation occurs, based on user behavior and objectives. It has two input resources: the data that are collected from sensors and objects and stored and the data that are received from the intentions and behaviors of the user. As an output, this step translates commands into the specified language of each component and generates motions, trajectories and visual feedback. It requires high computational capabilities, an embedded platform and AI-based functionalities. Meanwhile, it also uses an IoT bridge for internal and external data transmission and exchange.Step Five (“Simulate”): The algorithms that are generated during the Process step need to be simulated before being transferred to physical devices. Simulation has multiple purposes:Simulate the planned behavior and processes;Predict errors and prevent problems before they happen;Optimize and/or validate the simulated processes;Remote assistance, maintenance and monitoring.It also has many benefits, e.g., in robot programming, the simulation of the movements of a robot before deploying them to the physical robot can increase the iteration time by disclosing hidden outcomes or experimenting with edge movements that may be critical for the physical robot to act directly. Furthermore, the simulation is carried out using MR immersive capabilities. During this step, the user can move around objects so that they can obtain a better preview. In addition, they can interact with objects, send feedback to the system through the immersive interface and validate the processed operations that are to be executed on real physical machines.Step Six (“Act”): This is the execution of the planned and/or simulated processes by physical devices or machines. The system translates the generated motions into commands that the physical device interfaces can understand. The commands are then transmitted through the IoT bridge.The proposed DT-HRI method aims to improve upon the current human–robot interactions, robot simulation and robot programming method due to the use of emerging technologies that can be used to fit into smart factory exigencies and demands. For this use case, the system was composed of two pieces of physical equipment: a collaborative robot and an MR head-mounted device (MR-HMD). The physical world consisted of human beings, one or more collaborative robots, an MR-HMD for each user and, when needed, application-related objects . The digital world, on the other hand, contained the digital twin model of the robot, additional virtual objects and the user interactive interface (UII). The digital world could recognize and consider human gestures, voices and movements. A third-party engine was responsible for the data collection and processing, along with the generation of the algorithm.The HRI-DT framework is illustrated in The flowchart presented in Manual Manipulation: The operator used the UII to move the robot arm in the same way as the online programming methods, using either the teach pendant or PbD approach. The difference when using online programming for the proposed DT-HRI approach was that the work was performed on the virtual robot and a simulation preview was available, so the operator could choose to either approve or reject the planned job.Autonomous Decision-Making: A broker–processor received the intentions of the user, analyzed the environmental status of both worlds and then generated algorithms for either an action to be taken by a physical entity or feedback to be shown to the user. The decision that was made was first simulated in the digital world before being transmitted to a physical entity after approval.In the selected scenario, two types of manipulation were possible:The broker had different ROSbridge nodes that were responsible for the IoT communication patterns with different components. The system and its implementation are described in the next paragraph.An ROS communication system is composed of a centralized pattern involving an ROSmaster and multiple ROSbridge nodes. The system has three layers: DT middleware, a physical device and digital device layers.Data that are collected from and delivered to both device layers  file of each mechanical object was imported into the platform. The URDF XML format described the structural illustration of the KUKA IIWA robot and the attached 2F gripper. Furthermore, the same URDF description was used by ROS to communicate between the physical and digital objects using ROS messages. On the Unity side, the ROSsharp library was used to establish communication with the ROSbridge Unity node in the broker using TCP WebSockets. The Unity MixedReality-Toolkit 2 (MRTK2) was used, in addition to some other libraries and APIs.Project Initiation: After finishing the programming phase, the application was ready to run. First, the operator needed to launch the system by linking the real and digital worlds using the immersive MR head-mounted device. Thanks to the depth sensor, IMU motion sensor and integrated camera on the Hololens 2 device, the spatial mapping of the real environment was provided. The link was then made using an initial calibration that enabled a connection between the coordinate frame of the Hololens 2 device and the real frame of the robot. In our use case, the calibration was performed using an external Vuforia SDK . The appThere were many other possibilities that were tested, such as AI-based object recognition algorithms and QR code scanning, but the image target method from Vuforia was selected because of its simplicity, efficiency and ease of implementation. Once the operator put the Hololens 2 device on and launched the app, the device started the spatial scanning of the real world. As soon as the target was detected, the previously implemented virtual objects appeared in the holographic lenses as though they were real.3.Model Superimposition: The superimposition of the digital twin of the robot was a critical phase for accurate and efficient simulation results. First, the digital twin had to be overlaid onto its physical twin. By scanning and detecting the Vuforia camera-based image target during the project initiation phase, as shown in 4.Holographic Visualization and Interaction: The visualization phase enabled the user to interact with the digital content through the immersive holographic interface.Interactions were conducted through the user’s hand gestures via the hardware (camera and IMU motion sensor) and software (MRTK2) capabilities of the MR-HMD. Different control panels were implemented, depending on the task, e.g., synchronization, simulation, online programming using manual manipulation or autonomous programming. 5.Model Training, Object Pose Estimation and Motion Planning: The model training and motion planning nodes aimed to determine the target position and orientation, called pose estimation, as well as the joint position of the robot. This information was calculated using the ROS-based broker, as shown in The autonomous decision-maker broker, which is presented in An AI-based algorithm was integrated into the system and used in the use case. The selected algorithm was a deep conventional neural network (DCNN), which was adapted from . It aimeA major benefit of using the virtual world is the creation of training models in a manageable and personalized way. It also affords automatic data annotation that can be systematically validated. Thanks to its Perception Package, Unity is able to generate large-scale datasets for model training and validation by applying domain randomization, which adjoin ground truth annotations for every captured frame. Randomized parameters provide more variations in the produced data than training a model in a particular rigid environment. The randomized parameters in our use case were cube position and orientation, light direction and light color. The collected data in the use case were RGB images that were taken by the main Unity camera with a specific resolution and 3D bounding boxes, which were labeled scene objects. Thousands of pictures were captured, labeled and stored. Next, the dataset that was gathered from the virtual environment was used to train the DCNN model to find the target position and rotation. The applied model was adapted and modified from . Its arc6.Simulation: The simulation phase is not mandatory, but it is one of the benefits of the proposed method. Users could visualize the planned movements being executed on the virtual robot before they were transmitted to the real robot. Simulation is beneficial while working in hybrid teams. It reduces the defects of the robot and nearby equipment and maintains operator safety. It also permits real-time simulation in real environments, which cannot be achieved through traditional simulation methods that use monitors or VR-based methods.7.Validation: Once the operator agreed to a simulation, it could be validated by pressing the “Apply Movements” button on the interface. Validation meant that the simulated movements could be transmitted and executed by the real robot in the real world.8.Outcome Transmission: After the validation, the simulated outcomes were transferred to the broker using ROSbridge, where they were processed and transformed into robotic commands.The results from the use of the proposed DT-HRI framework in a use case are presented in this section.The main objective of this study was to apply the proposed DT method to a realistic use case to evaluate its performance. The described system was implemented, deployed using the Hololens 2 device and then demonstrated. The goals of the approach could fail for many reasons, such as the system configuration, real-time communication between the physical and digital worlds, autonomous decision-making prospects or system reconfiguration flexibility. Once deployment was complete, the operator could simulate and program the robot without any previous programming knowledge just by using hand gestures to interact with the robot through the immersive interface.Communication is a critical point that should be maintained and efficient throughout the system process. During the first Connect step, the digital and physical twins needed to be connected and able to send and receive data in real time. The ROS-based communication interfaces were well established and tested. Once the master was initiated, the robot controller was connected and started its waiting loop for received requests, then it started publishing. In the same way, the digital twin was also configured and connected via the IoT gateway. All connections were made through the TCP/IP connection of the IoT gateway.The collection of data from physical twin was performed by clicking the “Synchronize” button, as shown in While trying to combine both worlds, the system used first image target recognition to position the digital environment within the real world, so that it overlaid the physical twin. The stability of the visualized holograms after the image target scanning was evaluated and an average displacement error of ±1 to 2 cm was detected between the two bases of the robots while moving around them. Taking into consideration the size of the objects, this error did not impact the pick and place tasks, especially when using the 2-finger gripper. Using advances in hardware capabilities, software APIs and detection algorithms, this error could be reduced.Once the digital world was set up and obtained its position from the real world, the user could start the interaction and simulation process. Firstly, the user needed to choose the type of operation: either manual or autonomous manipulation. The manual manipulation of the robot involved the user applying either forward or inverse kinematic robot movements through the Hololens UX interface, as shown in . OtherwiTo pick and place the cube in the desired position, the user used hand gestures to move the small cube representing the target position to the desired position, as shown in As for future work, AI-based algorithms, as well as the spatial awareness capability of the Hololens 2 device, will be tested to replace the Vuforia image target for the digital model superimposition to reduce displacement errors. Furthermore, thanks to the flexibility of the DT-HRI concept, more demonstrators will be built using different kinds of robots, such as mobile robots, universal robots, etc. The framework will also be extended to implement more tasks, such as collaborative assembly and disassembly operations, resolving shape puzzles, stacking objects of different shapes, etc.The proposed DT-HRI demonstrator was tested by people who were trying to program the IIWA robot for the first time and total agreement was received from all participants regarding the ease of interaction with the robot without any previous knowledge or training.The introduction of Industry 4.0 technologies has reshaped the old form of manufacturing. Despite the existence of technologies such as IoT, CPS, AI and collaborative and autonomous robots in industrial environments and even though the main objective of Industry 4.0 is to implement better connected, more flexible and smarter industrial environments, some aspects still need to be better integrated and implemented. Among these aspects are human–robot interactions, collaborative robot programming and simulation, which still need many improvements in order to fit in with new smart environments in which robots and humans work together in hybrid teams.Common CPS, as well as DT systems, are currently used for either offline virtual simulation or for linking digital and physical twins. MR technology is commonly used for visualization tasks, such as enhanced maintenance or remote assistance. IoT communication designs are well integrated and provide real-time communication but, at the same time, are still complex when developing or integrating new devices. The evolution of collaborative robots ought not to exclude humans but to facilitate their work and enhance their efforts when needed.The proposed work envisioned the future of robot programming and robot simulation in industrial environments in which humans and robots work side by side in hybrid teams. The main objective of this work was to build and demonstrate a new digital twin framework, which was designed to enhance human–robot interactions, robot programming and simulation. The proposed approach would be required to create a flexible real-time service-based framework for both vertical and horizontal integration. It would also be needed to provide intuitive and human-friendly usage for unskilled workers.This paper introduced the six steps of the digital twin for the human–robot interaction framework, which was adapted and modified from the common 5-C architectural design of CPSs. Its flexible architecture granted the robust integration of new devices, systems and APIs. Since this framework was initially designed for human–robot interactions, its capabilities and implementation were demonstrated through a use case study. In all six steps, a horizontal technological architecture was used.Even though many hardware, as well as software, problems and challenges were faced during the development and demonstration of the use case, the major contributions of this research are (1) the proposal of a DT concept methodology for HRIs, (2) the application of the proposed method in a specific use case and (3) the implementation of the use case using a selection of hardware equipment, software, APIs and algorithms.The proposed system aims to (1) facilitate human–robot interactions and robot programming tasks so that they are feasible for any unskilled worker and (2) provide more realistic and efficient simulations in a real environment under real conditions.


Countries that aimed for eliminating the cases of COVID-19 with test-trace-isolate policy are found to have lower infections, deaths, and better economic performance, compared with those that opted for other mitigation strategies. However, the continuous evolution of new strains has raised the question of whether COVID-19 eradication is still possible given the limited public health response capacity and fatigue of the epidemic. We aim to investigate the mechanism of the Zero-COVID policy on outbreak containment, and to explore the possibility of eradication of Omicron transmission using the citywide test-trace-isolate (CTTI) strategy.We develop a compartmental model incorporating the CTTI Zero-COVID policy to understand how it contributes to the SARS-CoV-2 elimination. We employ our model to mimic the Delta outbreak in Fujian Province, China, from September 10 to October 9, 2021, and the Omicron outbreak in Jilin Province, China for the period from March 1 to April 1, 2022. Projections and sensitivity analyses were conducted using dynamical system and Latin Hypercube Sampling/ Partial Rank Correlation Coefficient (PRCC).CI: 28–33) days, after 10 (95% CI: 9–11) rounds of citywide testing. The emerging Jilin Omicron outbreak may achieve zero COVID cases in 50 (95% CI: 41–57) days if supported with sufficient public health resources and population compliance, which shows the effectiveness of the CTTI Zero-COVID policy.Calibration results of the model estimate the Fujian Delta outbreak can end in 30 (95% confidence interval The CTTI policy shows the capacity for the eradication of the Delta outbreaks and also the Omicron outbreaks. Nonetheless, the implementation of radical CTTI is challenging, which requires routine monitoring for early detection, adequate testing capacity, efficient contact tracing, and high isolation compliance, which constrain its benefits in regions with limited resources. Moreover, these challenges become even more acute in the face of more contagious variants with a high proportion of asymptomatic cases. Hence, in regions where CTTI is not possible, personal protection, public health control measures, and vaccination are indispensable for mitigating and exiting the COVID-19 pandemic.The online version contains supplementary material available at 10.1186/s40249-022-01030-7. Since the first COVID-19 case was reported in 2019, new variants have been found in different parts of the world. Many of them were classified as Variants of Concern (VOC) due to the higher transmissibility and lower response to vaccination and public health measures . Some coThe Zero-COVID strategy includes measures such as mass testing, detailed contact tracing using the most advanced technologies, and strict control measures upon detection of new cases, and this strategy appears to be more beneficial than less stringent measures , 7, 8. OThere have been modeling studies –11 that China has implemented the Zero-COVID policy from the first outbreak in January of 2020, and since then till early March, 2022, all of the local outbreaks caused by imported cases of wildtype have been controlled by this national zero-tolerance policy . Once a The first Omicron case was imported to the mainland of China on December 9, 2021, and due to its stronger transmissibility, the eradication of COVID-19 has become more difficult . On MarcWe propose a Susceptible-Exposed-Asymptomatic-Infectious-Recovered (SEAIR) model that mimics the implementation of the CTTI Zero-COVID policy in curbing the local transmission in Fujian Province and Jilin Province, China, using the data of daily new confirmed cases, including symptomatic and asymptomatic infections  , 31. We Free transmission stage”. Once the infection is confirmed, we consider the ideal scenario that the first round of CTTI is immediately conducted. From this point, we define the “Contained transmission stage” in which the Zero-COVID policy is implemented. We define We present our compartmental model incorporating the CTTI under the Zero-COVID policy as shown in Fig. We apply our model to estimate the number of testing rounds needed to achieve zero transmission for Fujian Province after calibrating the model using epidemiology data. We then estimate the rounds of citywide testing, cumulative cases, and in particular, the total number of isolated individuals under different free-transmission periods, testing capacities, and contact tracing efficiencies. In addition, we present the projections of the recent outbreak resulting from the Omicron transmission in Jilin province till April 30, 2022, under different scenarios. Furthermore, the uncertainty of parameters estimation is discussed by the sensitivity analysis.The first reported infection of the Delta variant of COVID-19 was detected in the routine testing of a primary school in Putian, a city in southeastern coastal of Fujian, on September 10, 2021, which was linked to the importation of cases from Singapore. It quickly ballooned into a province-wide outbreak , mostly Here, we also apply our model to the recent Omicron outbreak that occurred in Jilin Province, China, using the data of daily new confirmed cases, including symptomatic and asymptomatic infections, from March 1, 2022, to April 1, 2022 .The comprehensive and timely contact tracing serves as one of the crucial control measures in curbing the transmission of the COVID-19 epidemic. In February 2020, China rolled out its “health code” app nationwide , while the other zones implement 5:1 or 10:1 pooled testing [the third edition of Guidelines for Regional Nucleic Acid Testing was issued with a specified requirement for completing citywide testing within 24 h [The rolling out citywide testing  as it battles the outbreak can be such a powerful tool for getting on top of the virus. In China, one round of citywide testing takes several days, depending on the population and testing capacity in the city, usually 2–3 days . Howeverhin 24 h .R—Deceased D model framework. When the cases are detected, we also include the diagnosed and isolated We investigate the effect of the Zero-COVID strategy using a deterministic compartmental Susceptible We model the transmission process starting with local people infected by the imported virus and ending with zero COVID cases. Two stages before and after the detection of the first confirmed cases at the time mentclass2pt{minimWe further denote There are three separative testing in the contained transmission stage: symptom-driven testing, citywide testing, and the testing for primary and secondary contacts at the designated isolation facilities. And We define Therefore, the number of primary contacts and secondary contacts of newly diagnosed infections from citywide testing at time We assume that the symptomatic infections are already detected by symptom-driven testing. Hence, the traced population is composed of susceptible, exposed, asymptomatic, and presymptomatic individuals. The number of the traced individuals that are exposed is denoted as Similarly, we can obtain the number of traced presymptomatic infections, which isThe number of traced asymptomatic infections isThe number of traced susceptible individuals isTherefore, the traced population of confirmed cases from citywide testing are the sum of the above, i.e.,Testing for the traced population is conducted separately and has a higher frequency compared with citywide testing. The number of detected people from testing for those traced population at time We do not consider the contact tracing for The symptomatic infectious individuals The number of individuals who will get tested in this current round of citywide testing at time Similarly, we can obtain that the presymptomatic infectious individuals Therefore, the number of daily new diagnosed cases at time The flow chart of the model in the free transmission stage is presented in Fig. At time Based on our previous analysis, we have the model in the contained transmission stage where the CTTI strategy is conducted, and its flow chart is shown in Fig. Then the initial state at Starting from So, the model on the CI) of the estimated parameters are obtained through 1000 best-fitting parameters vectors  . Data anTo study the sensitivity of the CTTI policy-related parameters on the model outputs, such as cumulative cases and isolated people, we use the Latin Hypercube Sampling/Partial Rank Coefficient (LHS/PRCC) method , generatCI: 430–567) infections after 10 (95% CI: 9–11) rounds of citywide testing.Here, we investigate how the CTTI strategy Correlation works in controlling the local outbreak using the outbreak in September 2021 in Fujian as a case study. The model calibration results using the data from the Fujian outbreak are shown in Fig. We also observe that the epidemic progression is confined, along with the increased total number of isolated people. When the cumulative isolated people reach a plateau, all the possible infectious people are isolated, and local cases are eliminated. The number of cumulative isolated people can serve as a novel yet effective indicator to measure the effort of the public health sector to eradicate the local outbreak, achieving zero community transmission. With the aggressive Zero-COVID policy, the containment of the Delta virus in Fujian will only take 30 days. This result signals the efficiency of the CTTI policy resulting in a quick curbing of the local transmission.We investigate the impact of the CTTI strategy if early detection to confirm the first case is missed or postponed Fig. . We assuOn the other hand, the considerable effect of the CTTI strategy is also possible in regions where a large outbreak is ongoing (the following case of Jilin). It still may successfully curb the transmission, but with more resources. In fact, this strategy can mitigate and reduce the wave trend by isolating not just cases, but also their contacts and, most importantly, asymptomatic cases, which run the risk of being undetected if a strict testing procedure is not realized.We explore the effect of test capacity and contact tracing, heavily relying on the public health resources, on eliminating transmission under the assumption of 8 days free transmission stage Fig. . We obseIn addition, effective contact tracing will shorten the time needed to eliminate the local epidemic. If one round of citywide test is finished in 4 days  and contact tracing targeted . We find that the tracing targeted strategy is more efficient in containing the local outbreak. The tracing targeted strategy ends the epidemic 13 days earlier with fewer infections (30% decrease), though more isolated people  if the compliance rate of citywide testing in Jilin increase to 90% and the 90% of close contacts can be traced and isolated in 24 h  and, if applied promptly, is able to end an outbreak in a short time, also for the contagious Omicron variant. But this comes with high social and economic costs, which constrain its applicability to other regions. In fact, the effectiveness of the CTTI strategy is further enhanced when combined with timely early case detection. However, the rapid implementation of citywide testing is not the unique measure needed to reduce the local transmission. Efficient contact tracing and isolation of primary and secondary contacts of confirmed cases are also essential to cut off the local transmission. Moreover, cities or regions with limited resources may prioritize the allocation of resources to contact tracing to help control the epidemic.The CTTI strategy can efficiently eliminate the local transmission, which does not rely on the vaccine availability, the state of the epidemic, and the progression of the disease. This aggressive control strategy breaks the local transmission chain by isolating all the possible infection resources through citywide testing and contact tracing, hence, it can bring any infectious disease epidemic to an end mathematically. The decline in the number of daily new isolated people through testing and tracing indicates that the epidemic is gradually being controlled. Without perfect vaccines, the CTTI policy is the optional way of controlling the outbreak and a possible eradication strategy. However, the public health resources and administration capacity used in eradicating the virus were tremendous. More than 40,000 individuals were isolated, and almost 90 million tests were conducted in the containment of Fujian outbreak in September 2021 . The socThe enforcement of the CTTI strategy is hesitated by authorities due to the high daily testing volume. However, there is the argument that mass testing is feasible even in low-resource rural settings if it meets the requirements of minimal equipment and training . In counThe countries that opted for mitigation strategies, like Europe, which is the epicenter of COVID pandemic, are facing a worrying resurgence in COVID cases . SingapoHowever, the applicability of the Zero-COVID strategy is doubted, and it is criticized for overreacting to the epidemic and the substantial social and economic cost. It is argued that it is worthwhile to test millions of people to detect several cases. Especially in the later controlled stage, keeping tests seems to have no benefit to the containment of the epidemic. The discontent of populations may be increased along with the repeated testing, and the compliance rate of testing and isolation will be affected by the repeated outbreaks. Hence, the CTTI strategy is an efficient way to control the epidemic, but the optimal way of containment may still need further investigations. On the other hand, the prolonged prevalence of the epidemic may require considerable public health resources and result in immense economic loss. It is difficult to compare the cost between elimination with extensive resources in a short period and mitigation with relatively fewer resources but a more extended prevalence. Further studies in terms of economic assessment may shed some light on this comparison.Moreover, the high coverage rate of vaccination should be a vital step in the exit strategy. The mitigation of the epidemic is seen with the increase in vaccine coverage. The transmission risk decreases with the vaccination rollouts, although it is challenged by the keep emerging new variants, such as the Delta and Omicron variants , 48. ButOur analysis has several limitations. Firstly, we do not consider the different testing strategies in the varying levels of risk zones. In the later stage of elimination, the citywide testing has low performance with high cost. Then, only the people in the high-risk zone are tested according to the actual implementation. Our model may overestimate the rounds of CTTI needed due to the spatial heterogeneity. One way is to use individual based modelling or use meta-population models, however this type of spatial modelling would be too complex since we need to define the contact transmission matrix to take care of different population groups and spatial variations in the region considered. We believe that the broad applied mathematics community will continue to seek solutions to use spatial modelling with certain level of heterogeneity to fit the data. We will keep it as our future work too. One other limitation is the vaccination not considered. All the individuals need to do the testing regardless of the vaccination status. The reduced transmission risk is included in its estimation process. Nevertheless, the neglect of the vaccination may also overestimate the resources needed to eliminate the epidemic. In addition, the overlap between the primary contacts and the secondary contact is not considered in the model. The primary contacts of confirmed cases may have contact with each other, and then the number of traced secondary contacts will be reduced. However, it is not an easy task to determine the actual number of primary and secondary contacts, hence we are assuming the average contacts of each person. This simplification does not affect our contact tracing process.In summary, our results highlight the importance and efficiency of the CTTI Zero-COVID policy for the containment of the COVID-19 epidemic, by which even the current more aggressive Omicron outbreaks can be contained. Utilizing sufficient resources and early detection of the epidemic, the rapid implementation of the Zero-COVID policy with effective contact tracing, isolation of primary and secondary contacts, the CTTI policy can ensure the elimination of COVID-19 in a short period. But the applicability of CTTI policy to regions with limited resources is constrained, although its partial implementation can help alleviate the epidemic. However, if the outbreak is not wholly eliminated, the resurgence may be experienced in the local area. The combination of CTTI and vaccine may be the feasible exit strategy. Our results also highlight the urgent need for efficient tests, comprehensive contact tracing, and isolation compliance to support the mitigation of global pandemics of COVID.Additional file 1: The supporting materials of implementation of contact tracing in China, the estimated parameters in Fujian case, the initial values of state variables and parameters used in Jilin case and the sensitivity analysis on the number of daily cases and isolated individuals.