Influence of transportation network on transmission heterogeneity of COVID-19 in China

Prevention and control of infectious disease transmission in subways: an improved susceptible-exposed-infected-recovered model

Introduction

A well-connected transportation network unites localities but also accelerates the transmission of infectious diseases. Subways-an important aspect of daily travel in big cities-are high-risk sites for the transmission of urban epidemics. Intensive research examining the transmission mechanisms of infectious diseases in subways is necessary to ascertain the risk of disease transmission encountered by commuters.

Methods

In this study, we improve the susceptible-exposed-infected-recovered (SEIR) model and propose the susceptible-exposed-infected-asymptomatic infected (SEIA) model. First, we added asymptomatic patients to the improved model as a parameter to explore the role of asymptomatic patients in the transmission of infectious diseases in a subway. The numbers of boarding and alighting passengers were added to the model as two time-varying parameters to simulate the exchange of passengers at each station.

Results

The improved model could simulate the transmission of infectious diseases in subways and identify the key factors of transmission. We then produced an example of the transmission of coronavirus disease (COVID-19) in a subway using real subway passenger data substituted into the model for the calculations.

Discussion

We ascertained that the number of exposed people continuously increased with the operation of the subway. Asymptomatic patients had a greater impact on the transmission of infectious diseases than infected people in the course of transmission. The SEIA model constructed in this study accurately determined the spread of infectious diseases in a subway and may also be applicable to studies on the transmission of infectious diseases in other urban public transport systems.

Mapping the Characteristics of Respiratory Infectious Disease Epidemics in China Based on the Baidu Index from November 2022 to January 2023

Introduction

Infectious diseases pose a significant global health and economic burden, underscoring the critical need for precise predictive models. The Baidu index provides enhanced real-time surveillance capabilities that augment traditional systems.

Methods

Baidu search engine data on the keyword "fever" were extracted from 255 cities in China from November 2022 to January 2023. Onset and peak dates for influenza epidemics were identified by testing various criteria that combined thresholds and consecutive days.

Results

The most effective scenario for indicating epidemic commencement involved a 90th percentile threshold exceeded for seven consecutive days, minimizing false starts. Peak detection was optimized using a 7-day moving average, balancing stability and precision.

Discussion

The use of internet search data, such as the Baidu index, significantly improves the timeliness and accuracy of disease surveillance models. This innovative approach supports faster public health interventions and demonstrates its potential for enhancing epidemic monitoring and response efforts.

Geoepidemiological perspective on COVID-19 pandemic review, an insight into the global impact

The COVID-19 pandemic showed major impacts, on societies worldwide, challenging healthcare systems, economies, and daily life of people. Geoepidemiology, an emerging field that combines geography and epidemiology, has played a vital role in understanding and combatting the spread of the virus. This interdisciplinary approach has provided insights into the spatial patterns, risk factors, and transmission dynamics of the COVID-19 pandemic at different scales, from local communities to global populations. Spatial patterns have revealed variations in incidence rates, with urban-rural divides and regional hotspots playing significant roles. Cross-border transmission has highlighted the importance of travel restrictions and coordinated public health responses. Risk factors such as age, underlying health conditions, socioeconomic factors, occupation, demographics, and behavior have influenced vulnerability and outcomes. Geoepidemiology has also provided insights into the transmissibility and spread of COVID-19, emphasizing the importance of asymptomatic and pre-symptomatic transmission, super-spreading events, and the impact of variants. Geoepidemiology should be vital in understanding and responding to evolving new viral challenges of this and future pandemics.

A new approach to COVID-19 data mining: A deep spatial-temporal prediction model based on tree structure for traffic revitalization index

The outbreak of the COVID-19 epidemic has had a huge impact on a global scale and its impact has covered almost all human industries. The Chinese government enacted a series of policies to restrict the transportation industry in order to slow the spread of the COVID-19 virus in early 2020. With the gradual control of the COVID-19 epidemic and the reduction of confirmed cases, the Chinese transportation industry has gradually recovered. The traffic revitalization index is the main indicator for evaluating the degree of recovery of the urban transportation industry after being affected by the COVID-19 epidemic. The prediction research of traffic revitalization index can help the relevant government departments to know the state of urban traffic from the macro level and formulate relevant policies. Therefore, this study proposes a deep spatial-temporal prediction model based on tree structure for the traffic revitalization index. The model mainly includes spatial convolution module, temporal convolution module and matrix data fusion module. The spatial convolution module builds a tree convolution process based on the tree structure that can contain directional features and hierarchical features of urban nodes. The temporal convolution module constructs a deep network for capturing temporal dependent features of the data in the multi-layer residual structure. The matrix data fusion module can perform multi-scale fusion of COVID-19 epidemic data and traffic revitalization index data to further improve the prediction effect of the model. In this study, experimental comparisons between our model and multiple baseline models are conducted on real datasets. The experimental results show that our model has an average improvement of 21%, 18%, and 23% in MAE, RMSE and MAPE indicators, respectively.

Relationships between COVID-19 and disaster risk in Costa Rican municipalities

The COVID-19 pandemic has had far-reaching impacts on every aspect of human life since the first confirmed case in December 2019. Costa Rica reported its first case of COVID-19 in March 2020, coinciding with a notable correlation between the occurrence of disaster events at the municipal scale over the past five decades. In Costa Rica, over 90% of disasters are hydrometeorological in nature, while geological disasters have caused significant economic and human losses throughout the country's history. To analyze the relationship between COVID-19 cases and disaster events in Costa Rica, two Generalized Linear Models (GLMs) were used to statistically evaluate the influence of socio-environmental parameters such as population density, social development index, road density, and non-forested areas. The results showed that population and road density are the most critical factors in explaining the spread of COVID-19, while population density and social development index can provide insights into disaster events at the municipal level in Costa Rica. This study provides valuable information for understanding municipal vulnerability and exposure to disasters in Costa Rica and can serve as a model for other countries to assess disaster risk.

Causal effects of mobility intervention policies on intracity flows during the COVID-19 pandemic: The moderating role of zonal locations in the transportation networks

Many studies have investigated the impact of mobility restriction policies on the change of intercity flows during the outbreak of COVID-19, whereas only a few have highlighted intracity flows. By using the mobile phone trajectory data of approximately three months, we develop an interrupted time series quasi-experimental design to estimate the abrupt and gradual effects of mobility intervention policies during the pandemic on intracity flows of 491 neighborhoods in Shenzhen, China, with a focus on the role of urban transport networks. The results show that the highest level of public health emergency response caused an abrupt decline by 4567 trips and a gradually increasing effect by 34 trips per day. The effectiveness of the second return-to-work order (RtW2) was found to be clearly larger than that of the first return-to-work order (RtW1) as a mobility restoration strategy. The causal effects of mobility intervention policies are heterogenous across zonal locations in varying urban transport networks. The declining effect of health emergency response and rebounding effect of RtW2 are considerably large in better-connected neighborhoods with metro transit, as well as in those close to the airport. These findings provide new insights into the identification of pandemic-vulnerable hotspots in the transport network inside the city, as well as of crucial neighborhoods with increased adaptability to mobility interventions during the onset and decline of COVID-19.

Systematic literature review on impacts of COVID-19 pandemic and corresponding measures on mobility

The unprecedented COVID-19 outbreak has significantly influenced our daily life, and COVID-19's spread is inevitably associated with human mobility. Given the pandemic's severity and extent of spread, a timely and comprehensive synthesis of the current state of research is needed to understand the pandemic's impact on human mobility and corresponding government measures. This study examined the relevant literature published to the present (March 2023), identified research trends, and conducted a systematic review of evidence regarding transport's response to COVID-19. We identified key research agendas and synthesized the results, examining: (1) mobility changes by transport modes analyzed regardless of government policy implementation, using empirical data and survey data; (2) the effect of diverse government interventions to reduce mobility and limit COVID-19 spread, and controversial issues on travel restriction policy effects; and (3) future research issues. The findings showed a strong relationship between the pandemic and mobility, with significant impacts on decreased overall mobility, a remarkable drop in transit ridership, changes in travel behavior, and improved traffic safety. Government implemented various non-pharmaceutical countermeasures, such as city lockdowns, travel restrictions, and social distancing. Many studies showed such interventions were effective. However, some researchers reported inconsistent outcomes. This review provides urban and transport planners with valuable insights to facilitate better preparation for future health emergencies that affect transportation.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11116-023-10392-2.

Responsive strategies for new normal cold supply chain using greenfield, network optimization, and simulation analysis

The global-local supply chains are affected by the forward and downward propagation of COVID-19. The pandemic disruption is a low-frequency and high-impact (black swan) event. Adapting to the "New Normal" situation requires adequate risk mitigation strategies. This study proposes a methodology to implement a risk mitigation strategy during supply chain disruptions. Random demand accumulation strategies are considered to identify the disruption-driven challenges under different pre and post-disruption scenarios. The best mitigation strategy and the optimal location of distribution centers to maximize the overall profit were determined using simulation-based optimization, greenfield analysis, and network optimization techniques. The proposed model is then evaluated and validated using appropriate sensitivity analysis. The main contribution of the study is to (i) perform cluster-based supply chain disruption analysis, (ii) propose a resilient and flexible model to illustrate the proactive and reactive measures for the ripple effect, (iii) prepare the supply chain for future pandemic-like crises, and (v) reveal the relationship between the pandemic impact and supply chain resilience. A case study of an ice cream manufacturer is used to demonstrate the proposed model.

COVID-19 public transit precautions: Trade-offs between risk reduction and costs

Public transit has received scrutiny as a vector for spreading COVID-19 with much of the literature finding correlations between transit ridership and COVID-19 rates by assessing the role that transportation plays as a vector for human mobility in COVID-19 spread. However, most studies do not directly measure the risk of contracting COVID-19 inside the public transit vehicle. We fill a gap in the literature by comparing the risk and social costs across several modes of transportation. We develop a framework to estimate the spread of COVID-19 on transit using the bus system in Pittsburgh. We find that some trips have demand that exceed their COVID-19 passenger limit, where the driver must decide between: (1) leaving a passenger without a ride or (2) allowing them on the bus and increasing COVID-19 risk. We consider five alternatives for alleviating overcapacity: allow crowding, additional buses, longer buses as substitutes, Transportation Network Company (TNC) rides, or Autonomous Vehicles (AVs) for passed-by passengers. We use transit ridership and COVID-19 data from the spring of 2020 by combining transportation data and an epidemiological model of COVID-19 stochastically in a Monte Carlo Analysis. Our results show that 4% of county cases were contracted on the bus or from a bus rider, and a disproportionate amount (52%) were from overcapacity trips. The risk of contracting COVID-19 on the bus was low but worth mitigating. A cost-benefit analysis reveals that dispatching AVs or longer buses yield the lowest societal costs of $45 and $46 million, respectively compared to allowing crowding ($59 million).

COVID-19 spread algorithm in the international airport network-DetArpds

Due to COVID-19, the spread of diseases through air transport has become an important issue for public health in countries globally. Moreover, mass transportation (such as air travel) was a fundamental reason why infections spread to all countries within weeks. In the last 2 years in this research area, many studies have applied machine learning methods to predict the spread of COVID-19 in different environments with optimal results. These studies have implemented algorithms, methods, techniques, and other statistical models to analyze the information in accuracy form. Accordingly, this study focuses on analyzing the spread of COVID-19 in the international airport network. Initially, we conducted a review of the technical literature on algorithms, techniques, and theorems for generating routes between two points, comprising an analysis of 80 scientific papers that were published in indexed journals between 2017 and 2021. Subsequently, we analyzed the international airport database and information on the spread of COVID-19 from 2020 to 2022 to develop an algorithm for determining airport routes and the prevention of disease spread (DetARPDS). The main objective of this computational algorithm is to generate the routes taken by people infected with COVID-19 who transited the international airport network. The DetARPDS algorithm uses graph theory to map the international airport network using geographic allocations to position each terminal (vertex), while the distance between terminals was calculated with the Euclidian distance. Additionally, the proposed algorithm employs the Dijkstra algorithm to generate route simulations from a starting point to a destination air terminal. The generated routes are then compared with chronological contagion information to determine whether they meet the temporality in the spread of the virus. Finally, the obtained results are presented achieving a high probability of 93.46% accuracy for determining the entire route of how the disease spreads. Above all, the results of the algorithm proposed improved different computational aspects, such as time processing and detection of airports with a high rate of infection concentration, in comparison with other similar studies shown in the literature review.

Insight into the nonlinear effect of COVID-19 on well-being in China: Commuting, a vital ingredient

Background

COVID-19 had a devastating impact on people's work, travel, and well-being worldwide. As one of the first countries to be affected by the virus and develop relatively well-executed pandemic control, China has witnessed a significant shift in people's well-being and habits, related to both commuting and social interaction. In this context, what factors and the extent to which they contribute to well-being are worth exploring.

Methods

Through a questionnaire survey within mainland China, 688 valid sheets were collected, capturing various aspects of individuals' life, including travel, and social status. Focusing on commuting and other factors, a Gradient Boosting Decision Tree (GBDT) model was developed based on 300 sheets reporting working trips, to analyze the effects on well-being. Two indicators, i.e., the Relative Importance (RI) and Partial Dependency Plot (PDP), were used to quantify and visualize the effects of the explanatory factors and the synergy among them.

Results

Commuting characteristics are the most critical ingredients, followed by social interactions to explain subjective well-being. Commuting stress poses the most substantial effect. Less stressful commuting trips can solidly improve overall well-being. Better life satisfaction is linked with shorter confinement periods and increased restriction levels. Meanwhile, the switch from in-person to online social interactions had less impact on young people's life satisfaction. Older people were unsatisfied with this change, which had a significant negative impact on their life satisfaction.

Conclusions

From the synergy of commuting stress and commuting time on well-being, the effect of commuting time on well-being is mediated by commuting stress in the case of China. Even if one is satisfied with online communication, the extent of enhancement on well-being is minimal, for it still cannot replace face-to-face interaction. The findings can be beneficial in improving the overall well-being of society during the pandemic and after the virus has been eradicated.

Impact of Different Transportation Modes on the Transmission of COVID-19: Correlation and Strategies from a Case Study in Wuhan, China

Transportation is the main carrier of population movement, so it is significant to clarify how different transportation modes influence epidemic transmission. This paper verified the relationship between different levels of facilities and epidemic transmission by use of the K-means clustering method and the Mann-Whitney U test. Next, quantile regression and negative binomial regression were adopted to evaluate the relationship between transportation modes and transmission patterns. Finally, this paper proposed a control efficiency indicator to assess the differentiated strategies. The results indicated that the epidemic appeared 2-3 days earlier in cities with strong hubs, and the diagnoses were nearly fourfold than in other cities. In addition, air and road transportation were strongly associated with transmission speed, while railway and road transportation were more correlated with severity. A prevention strategy that considered transportation facility levels resulted in a reduction of the diagnoses of about 6%, for the same cost. The results of different strategies may provide valuable insights for cities to develop more efficient control measures and an orderly restoration of public transportation during the steady phase of the epidemic.

Data analytics during pandemics: a transportation and location planning perspective

The recent COVID-19 pandemic once again showed the value of harnessing reliable and timely data in fighting the disease. Obtained from multiple sources via different collection streams, an immense amount of data is processed to understand and predict the future state of the disease. Apart from predicting the spatio-temporal dynamics, it is used to foresee the changes in human mobility patterns and travel behaviors and understand the mobility and spread speed relationship. During this period, data-driven analytic approaches and Operations Research tools are widely used by scholars to prescribe emerging transportation and location planning problems to guide policy-makers in making effective decisions. In this study, we provide a review of studies which tackle transportation and location problems during the COVID-19 pandemic with a focus on data analytics. We discuss the major data collecting streams utilized during the pandemic era, highlight the importance of rapid and reliable data sharing, and give an overview of the challenges and limitations on the use of data.

Bidirectional Causality between Spreading COVID-19 and Individual Mobilisation with Consumption Motives across Prefectural Borders in Japan

A combination of pharmaceutical and non-pharmaceutical interventions as well as social restrictions has been recommended to prevent the spread of coronavirus disease 2019 (COVID-19). Therefore, social contact surveys play an essential role as the basis for more effective measures. This study attempts to explore the fundamental basis of the expansion of COVID-19. Temporal bidirectional causalities between the numbers of newly confirmed COVID-19 cases (NCCC) and individual mobilisations with consumption motives across prefecture borders in three metropolitan regions in Japan were analysed using vector autoregression models. Mobilisation with consumption in pubs from Kanto to Tokai contributed to the spread of COVID-19 in both regions. Meanwhile, causal mobilisation with consumption motives in Kansai also contributed to the expansion of COVID-19; however, the pattern was dependent on the industrial characteristics of each prefecture in Kansai. Furthermore, the number of pub visitors in Kanto immediately decreased when NCCC increased in Kanto. In contrast, the causal mobilisations for the expansion of COVID-19 in the Tokai and Kansai regions were unaffected by the increasing NCCC. These findings partially proved the validity of the conventional governmental measures to suppress pub visitors across prefectural borders. Nevertheless, the individual causal mobilisations with consumption motives that contributed to the increasing COVID-19 cases are not identical nationwide, and thus, regional characteristics should be considered when devising preventive strategies.

The impact of the COVID-19 pandemic on O-D flow and airport networks in the origin country and in Northeast Asia

The ongoing COVID-19 pandemic has posed a global threat to human health. In order to prevent the spread of this virus, many countries have imposed travel restrictions. This difficult situation has dramatically affected the airline industry by reducing the passenger volume, number of flights, airline flow patterns, and even has changed the entire airport network, especially in Northeast Asia (because it includes the original disease seed). However, although most scholars have used conventional statistical analysis to describe the changes in passenger volume before and during the COVID-19 outbreak, very few of them have applied statistical assessment or time series analysis, and have not even examined how the impact may be different from place to place. Therefore, the purpose of this study was to identify the impact of COVID-19 on the airline industry and affected areas (including the origin-destination flow and the airport network). First, a Clustering Large Applications (CLARA) algorithm was used to group numerous origin-destination (O-D) flow patterns based on their characteristics and to determine if these characteristics have changed the severity of the impact of each cluster during the COVID-19 outbreak. Second, two statistical tests (the paired t-test and the Wilcoxon signed-rank test) were utilized to determine if the entire airport network and the top 30 hub airports changed during COVID-19. Four centrality measurement indices (degree, closeness, eigenvector, and betweenness centrality) of the airports were used to assess the entire network and ranking of individual hub airports. The study data, provided by The Official Aviation Guide (OAG) from December 2019 to April 2020, indicated that during the COVID-19 outbreak, there was a decrease in passenger volume (60%-98.4%) as well as the number of flights (1.5%-82.6%). However, there were no such significant changes regarding the popularity ranking of most airports during the outbreak. Before this occurred (December 2019), most hub airports were in China (April 2020), and this trend remain similar during the COVID-19 outbreak. However, the values of the centrality measurement decreased significantly for most hub airports due to travel restrictions issued by the government.

Managing public transit during a pandemic: The trade-off between safety and mobility

During a pandemic such as COVID-19, managing public transit effectively becomes a critical policy decision. On the one hand, efficient transportation plays a pivotal role in enabling the movement of essential workers and keeping the economy moving. On the other hand, public transit can be a vector for disease propagation due to travelers' proximity within shared and enclosed spaces. Without strategic preparedness, mass transit facilities are potential hotbeds for spreading infectious diseases. Thus, transportation agencies face a complex trade-off when developing context-specific operating strategies for public transit. This work provides a network-based analysis framework for understanding this trade-off, as well as tools for calculating targeted commute restrictions under different policy constraints, e.g., regarding public health considerations (limiting infection levels) and economic activity (limiting the reduction in travel). The resulting plans ensure that the traffic flow restrictions imposed on each route are adaptive to the time-varying epidemic dynamics. A case study based on the COVID-19 pandemic reveals that a well-planned subway system in New York City can sustain 88% of transit flow while reducing the risk of disease transmission by 50% relative to fully-loaded public transit systems. Transport policy-makers can exploit this optimization-based framework to address safety-and-mobility trade-offs and make proactive transit management plans during an epidemic outbreak.

Managing public transit during a pandemic: The trade-off between safety and mobility

During a pandemic such as COVID-19, managing public transit effectively becomes a critical policy decision. On the one hand, efficient transportation plays a pivotal role in enabling the movement of essential workers and keeping the economy moving. On the other hand, public transit can be a vector for disease propagation due to travelers' proximity within shared and enclosed spaces. Without strategic preparedness, mass transit facilities are potential hotbeds for spreading infectious diseases. Thus, transportation agencies face a complex trade-off when developing context-specific operating strategies for public transit. This work provides a network-based analysis framework for understanding this trade-off, as well as tools for calculating targeted commute restrictions under different policy constraints, e.g., regarding public health considerations (limiting infection levels) and economic activity (limiting the reduction in travel). The resulting plans ensure that the traffic flow restrictions imposed on each route are adaptive to the time-varying epidemic dynamics. A case study based on the COVID-19 pandemic reveals that a well-planned subway system in New York City can sustain 88% of transit flow while reducing the risk of disease transmission by 50% relative to fully-loaded public transit systems. Transport policy-makers can exploit this optimization-based framework to address safety-and-mobility trade-offs and make proactive transit management plans during an epidemic outbreak.

Geographical network model for COVID-19 spread among dynamic epidemic regions

Pandemic due to SARS-CoV-2 (COVID-19) has affected to world in several aspects: high number of confirmed cases, high number of deaths, low economic growth, among others. Understanding of spatio-temporal dynamics of the virus is helpful and necessary for decision making, for instance to decide where, whether and how, non-pharmaceutical intervention policies are to be applied. This point has not been properly addressed in literature since typical strategies do not consider marked differences on the epidemic spread across country or large territory. Those strategies assume similarities and apply similar interventions instead. This work is focused on posing a methodology where spatio-temporal epidemic dynamics is captured by means of dividing a territory in time-varying epidemic regions, according to geographical closeness and infection level. In addition, a novel Lagrangian-SEIR-based model is posed for describing the dynamic within and between those regions. The capabilities of this methodology for identifying local outbreaks and reproducing the epidemic curve are discussed for the case of COVID-19 epidemic in Jalisco state (Mexico). The contagions from July 31, 2020 to March 31, 2021 are analyzed, with monthly adjustments, and the estimates obtained at the level of the epidemic regions present satisfactory results since Relative Root Mean Squared Error RRMSE is below 15% in most of regions, and at the level of the whole state outstanding with RRMSE below 5%.

Suburban Road Networks to Explore COVID-19 Vulnerability and Severity

The Delta variant of COVID-19 has been found to be extremely difficult to contain worldwide. The complex dynamics of human mobility and the variable intensity of local outbreaks make measuring the factors of COVID-19 transmission a challenge. The inter-suburb road connection details provide a reliable proxy of the moving options for people between suburbs for a given region. By using such data from Greater Sydney, Australia, this study explored the impact of suburban road networks on two COVID-19-related outcomes measures. The first measure is COVID-19 vulnerability, which gives a low score to a more vulnerable suburb. A suburb is more vulnerable if it has the first COVID-19 case earlier and vice versa. The second measure is COVID-19 severity, which is proportionate to the number of COVID-19-positive cases for a suburb. To analyze the suburban road network, we considered four centrality measures (degree, closeness, betweenness and eigenvector) and core-periphery structure. We found that the degree centrality measure of the suburban road network was a strong and statistically significant predictor for both COVID-19 vulnerability and severity. Closeness centrality and eigenvector centrality were also statistically significant predictors for COVID-19 vulnerability and severity, respectively. The findings of this study could provide practical insights to stakeholders and policymakers to develop timely strategies and policies to prevent and contain any highly infectious pandemics, including the Delta variant of COVID-19.

Dynamic activity chain pattern estimation under mobility demand changes during COVID-19

During the coronavirus disease 2019 pandemic, the activity engagement and travel behavior of city residents have been impacted by government restrictions, such as temporary city-wide lockdowns, the closure of public areas and public transport suspension. Based on multiple heterogeneous data sources, which include aggregated mobility change reports and household survey data, this paper proposes a machine learning approach for dynamic activity chain pattern estimation with improved interpretability for examining behavioral pattern adjustments. Based on historical household survey samples, we first establish a computational graph-based discrete choice model to estimate the baseline travel tour parameters before the pandemic. To further capture structural deviations of activity chain patterns from day-by-day time series, we define the activity-oriented deviation parameters within an interpretable utility-based nested logit model framework, which are further estimated through a constrained optimization problem. By incorporating the long short-term memory method as the explainable module to capture the complex periodic and trend information before and after interventions, we predict day-to-day activity chain patterns with more accuracy. The performance of our model is examined based on publicly available datasets such as the 2017 National Household Travel Survey in the United States and the Google Global Mobility Dataset throughout the epidemic period. Our model could shed more light on transportation planning, policy adaptation and management decisions during the pandemic and post-pandemic phases.