: EpiMob System. It is an interactive visual analytics system for evaluating and simulating the effects of human mobility restriction policies for epidemic control. (A) enables the user to specify the mobility restriction policies like "region lockdown" and "telecommuting (work at home), and the simulation result about the transmission and infection situation will be displayed in policy overview panel (B) . Besides, user can do comparative analysis among policies, and the results will be displayed at (C).
The coronavirus disease 2019 (COVID-19) outbreak has swept more than 180 countries and territories since late January 2020, which has caused significant losses to public health as well as the economy at a worldwide scale. To respond to COVID-19 emergency, governments have taken various measures and policies such as self-quarantine, travel restriction, work at home, event canceling, and region lockdown to curb the rapid spread. As COVID-19 is a highly contagious disease with human-to-human transmission, the core purpose of these countermeasures is to conduct human mobility restrictions as possible as we can. How effective these policies could be becomes a significant and urgent question, especially for medical experts and policy makers. As thestate-of-the-art researches [15, 42] , the effects of mobility restriction policies taken at an early stage in China have been revealed. However, everyday the pandemic situation is still rapidly changing in the world, and governments need to flexibly implement different policies accord-ing to fundamental conditions of their country and gradually adjust their policies with the development of the epidemic. It is always necessary to demonstrate and simulate the actual effect of a certain restriction policy or a combination of policies in an easy and quick way. Thus, in this study, we design an interactive visual analytics system called EpiMob (Epidemic Mobility) based on big human mobility data and city POI data collected in Tokyo, the biggest city of Japan. Our system mainly focuses on two types of human mobility restriction policies, namely "close a region from community level to citywide level" and " from date A to date B", which are widely adopted and implemented by numerous governments in the world. The target is to demonstrate how the citywide human mobility as well as the number of infected people could change in light of user's different spatiotemporal settings. For instance, through EpiMob, we can easily do the epidemic simulations as follows: (1) starting to close the Setagaya Ward, one of 23 wards of Tokyo, from 2020-04-01; (2) starting work-from-home policy for the entire 23 wards of Tokyo from 2020-03-01.
In order to do so, we extend a normal numerical (Susceptible-Exposed-Infectious-Recovered) to a modified trajectory-based SEIR model. The SEIR model is a variant of the SIR (Susceptible-Infectious-Recovered) model, which is seen as one of the most fundamental compartmental models in epidemiology. The SEIR model consists of four compartments: S for the number of susceptible, E for the number of exposed, which means the individuals in an incubation period but not yet infectious, I for the number of infectious, and R for the number of recovered or deceased (or immune) individuals. To represent that the number of susceptible, infected and recovered individuals may vary over time (even if the total population size remains constant), we make the precise numbers a function of t (time): S(t), E(t), I(t) and R(t). For a specific disease in a specific population, these functions may be worked out in order to predict possible outbreaks and bring them under control. The SIR and SEIR model are reasonably predictive for infectious diseases that are transmitted from human to human, and where recovery confers lasting resistance, such as measles, mumps and rubella [1] . Moreover, spatial SIR and SEIR model could be built by meshing an area into a set of grids and setting the infection propagation from one grid to its surrounding neighbors. For instance, based on Baidu qianxi online service (China) [2], researchers first collected city-to-city inflow and outflow data (i.e., how many people moved from one city to another within one day), then they proposed a city-to-city spatial SEIR model to predict the COVID-19 epidemic peaks and sizes in China at a nationwide level [52] . The granularity of city-to-city aggregation data is coarse, so that this model is difficult to be applied to fine-grained simulation at a citywide level. Therefore, we propose a novel SEIR model that assumes that each person has a certain probability to get infected by the other persons inside the same grid at the same timestamp. Given the human trajectories of one city and a set of parameters, the epidemic simulation could be dynamically and continuously executed by calculating and updating our new SEIR model at a fixed time frequency (i.e., every 5 minutes in our case). EpiMob is a system that can interactively manipulate the modified SEIR model (i.e., setting inputs) and intuitively demonstrate the simulation results of the SEIR model (i.e., getting outputs). Each simulation essentially involves a set of human trajectories and model parameters. Given different human mobility restriction policies, we first generate a new set of restricted human trajectories via a mobility generative model, then feed the new trajectories plus new parameters to our SEIR model to trigger a new simulation. The main user interface of our EpiMob system is shown in Fig.1 . Users can specify the mobility restriction polices like "region lockdown" and "telecommuting (work at home)" through the console panel in the left, and the simulation result about how the transmission and infection situation will change will be displayed in the right. Users can also make spatial interactions like "close a polygonal region" or temporal interactions like "set time interval" through the right panel. Through multiple case studies for the biggest city of Japan (i.e.,Tokyo) and domain expert interviews, we demonstrate that our system can be beneficial to give an illustrative insight in measuring and comparing the effects of different human mobility restriction policies for epidemic control. To the best of our knowledge, EpiMob is the first interactive visual analytics system that can provide epidemic control policy simulation at fine-grained spatiotemporal granularity by utilizing citywide human mobility data and city POI data as inputs. The major contributions of our study are summarized as follows:
• We propose a novel trajectory-based SEIR model to simulate the epidemic spreading based on real-world big human trajectory data and city POI data.
• We design a "trajectory replacement" simulation strategy to handle the different settings on human mobility restrictions. Based on this strategy, we implement an online web system with a delicate and efficient system architecture.
• We provide a comfortable user interface with a set of new visualization techniques to visually and interactively help end user measure and compare the quantitative effects of different human mobility restriction policies.
• We evaluate our system through multiple case studies as well as interviews of domain experts and demonstrate the superior performance, functionality, and usability.
To help prevent the spread of COVID-19, researchers have done epidemic data analytics as well as developed the epidemic prediction model. For instance, an investigation of transmission control measures was conducted for the first 50 days of outbreak in China [42] . As one of the most effective mobility restriction policies, travel restriction and its effects were analyzed in [15] . [49] proposed a mathematical prediction model to nowcast and forecast the spread of COVID-19 inside and outside of China. Using Baidu Qianxi data (i.e., city-to-city inflow and outflow number) [2], modified SEIR and AI prediction model were proposed to predict the COVID-19 epidemic peaks and sizes [52] . [38] was specifically proposed to estimate the epidemiological parameters of prediction model. A trajectory-based algorithm has been proposed to efficiently detect suspected infected person from a large crowd of people [21] . Before the recent COVID-19 studies, epidemic-related studies have already been done in our visualization community. For example, VoroGraph [17] integrated a set of visualization tools for epidemic analysis; Epiviz [10] was an interactive visual analytics system designed for functional genomics data. However, these systems are not well tailored to our human-mobility-based epidemic control problem.
Human mobility has been analyzed through big trajectory data such as mobile phone GPS data or taxi GPS data. Researchers have proposed a family of algorithms to efficiently find different patterns from big trajectory database, such as "Convoy Pattern" [24] , "Swarm Pattern" [28] , and "Gathering Pattern" [55] . A robust and fast algorithm was proposed to discover similar trajectories given on query trajectory [11] . Meanwhile, mobility simulation at a citywide level has been a big challenge since the last decade. Brinkhoff generator [8] was proposed to generate and simulate network-based trajectories given the road network of a city. MNTG [33] extends [8] into a web-based traffic generator. SUMO [7] can simulate human mobility in a big urban area. MATSim (Multi-Agent Transport Simulation) [22] has been seen as the state-of-the-art solution for citywide traffic simulation in the filed of transportation engineering. By employing the machine learning technologies, data-driven methodologies have been proposed for mobility simulation or generation for a large urban area [6, 27, 34, 53] . Besides, a human mobility simulator was specifically developed for disaster situation (i.e., 2011 Great East Japan Earthquake) [40] . Simulating or generating the citywide human mobility under different restriction policies is still seen as a relatively underexplored topic.
Recent advances and challenges in information visualization are summarized in [32] . Especially, researchers have given an overview of visualization techniques on classic trajectory [5] , traffic flow [14, 39] , and urban computing [56] . As representative applications of visual analytics on spatiotemporal data, SmartAdP [30] was a visual analytics system for selecting billboard locations with trajectory data; AirVis [16] and [37] focused on visual analytics for air pollution problem. In particular, based on trajectory data, [45] did visual analysis for traffic jam problem; [4] extracted significant places; [31] explored route diversity; Trajgraph [23] studied urban network centralities. From a data perspective, visual analytics was done on new york city taxi data [18] , sparse bus trajectory data [36] , trajectory attribute data [43] , and origindestination trajectory data [57] . Moreover, as spatiotemporal data are high complex, many studies aimed to utilize visualization techniques to better understand big trajectory data or discover trajectory pattern. Mobilitygraphs [44] utilized graph and clustering to visually understand mass mobility dynamics; [13] focused on pattern discovering from geo-tagged social media data; Telcovis [50] explored co-occurrence pattern based on telco data; [20] aimed to provide pandemic decision support using spatial interaction patterns. Lastly, visualization techniques on spatiotemporal data are proposed for some special purposes. [41] embedded spatiotemporal information to map; [51] enriched geographical information to mobility flow; Location2vec [58] proposed a situation-aware visual representation of urban locations; R-Map [12] designed a map metaphor to understand reposting process in social media; Srvis [46] focused on ranking visualization for spatial information; Homefinder [47] aimed to find ideal home via visual analytics; SmartCube [29] was proposed for the real-time visualization of spatiotemporal data. Our study emphasizes on fitting the spatiotemporal visualization and interaction well into city-scale epidemic simulator.
In this section, we first introduce some basic concepts, describe the data source used in our study, and give the task analyses based on the discussion with domain experts.
To elaborate the problem, we formally define some terms related to citywide human mobility.
• Human Trajectory: The human trajectory collected for an individual person essentially comprises a 3-tuple sequence: (timestamp, latitude, longitude), which can indicate a person's location according to a captured timestamp. It can be further denoted as a sequence of (t, l)-pair attached with user ID uid by simplifying timestamp as t and (latitude, longitude) as l.
tra j = {uid, (t 1 , l 1 ), (t 1 , l 2 ), ..., (t n , l n )}
• Citywide Human Mobility: Citywide human mobility Γ refers to a large group of user trajectories in a given urban area. Given a use ID uid, we can retrieve his/her personal trajectory from Γ as follows: Γ uid = {(t 1 , l 1 ), (t 1 , l 2 ), ..., (t n , l n )}
• Grid-Mapped Interpolated Human Trajectory: The sampling rate of raw human trajectory data is usually unconstant. After applying a typical prepocessing method proposed in [25, 26] , we can get interpolated human trajectory with a constant sampling rate ∆τ as follows:
where ∆τ is set to 5 minutes in this study. Furthermore, we map the interpolated human trajectory onto mesh-grid as follows:
To this end, we have done preprocessing including interpolation and grid-based mapping to citywide human mobility data. Next, we formally illustrate how to run the epidemic simulation for different mobility restriction policies.
• Trajectory-Based Epidemic Simulation: We can do epidemic simulation with trajectory-based SEIR model F SEIR as follows:
where Γ is the given citywide human mobility, Θ refers to the parameters of SEIR model, and E s im denotes the simulation results including the infected trajectories and the infection number. Every time we give a set of (Γ, Θ) to the trajectory-based SEIR model, we could run the epidemic simulation in a new round.
• Mobility Restriction Policy: Our study focuses on evaluating and measuring the effects of different restriction policies. Specifically, we list some restriction policy terms as follows:
-Detection refers to setting up a infection detection point in a specific location like roadside or station to detect whether this person is infectious or not.
-Telecommuting is a corporate policy that allows employees to work from home using information and communications technologies instead of commuting to the office.
-Region Lockdown is a government policy that implements mandatory geographic quarantine to all of the citizens living in a specific region (city or ward).
• Restricted Mobility Generation: Given one mobility restriction policy or a combination of several policies Φ, citywide human mobility will forcibly change due to the given Φ. In our study, we utilize a mobility replacement model denoted as F MOB to generate the restricted human mobility Γ w.r.t Φ as follows:
• Epidemic Simulation with Restricted Mobility: Given the restricted citywide human mobility Γ w.r.t Φ and a set of new parameters Θ , epidemic simulation for the restriction policy settings E sim could be implemented as follows:
This reflects the key idea of our simulation strategy: (1) generating new citywide human trajectories for the given restriction policy settings;
(2) applying the trajectory-based SEIR model on the new generated trajectories.
To model real-world human mobility used for epidemic simulation, we collected a GPS log dataset anonymously from about 1.6 million real mobile-phone users in Japan over a three-year period (from August 1, 2010 to July 31, 2013) . This dataset contains about 30 billion GPS records, more than 1.5 TeraBytes. The data collection was conducted by a mobile operator (i.e., NTT DoCoMo, Inc.) and private company (i.e., ZENRIN DataCom Co., Ltd.) under the consent of mobile phone users. These data were processed collectively and statistically in order to conceal private information such as gender or age. By default, the positioning function on the users' mobile phones is activated every 5 minutes, so their positioning data (i.e., latitude and longitude) are uploaded onto the server. However, the data acquisition is affected by several factors such as loss of signal or low battery power. In addition, when a mobile phone user stops at a location, the positioning function of his/ is automatically turned off to save power. In this study, we select Greater Tokyo Area (including Tokyo City, Kanagawa Prefecture, Chiba Prefecture, and Saitama Prefecture) as the target area of epidemic simulation. The user ID will be selected as our experimental data if 80% of user's trajectory points locate in Greater Tokyo Area. After this, we can obtain 145507 users' trajectories in total that covers approximately 1% of the real-world population.
The distribution of POI (point of interest) has a strong relationship with the parameter settings of our SEIR simulation model. A quantitative characterization of the POI effects plays an important role in conducting real-world simulation. Therefore, we collected the Telepoint Pack DB of POI data in February 2011 provided by ZENRIN DataCom Co., Ltd [3]. In the original database, each record is a registered land-line telephone number with coordinates (latitude, longitude) and industry category information included. We treated each "telepoint" as one specific POI. All the POIs were classified into 40 categories. The total numbers of POIs for Tokyo is 281,400. We manually deleted some of unrelated categories retained five categories that are very relevant with epidemic simulation, namely "entertainment", "restaurant", "supermarket and shopping mall", "public place", and "subway and bus station".
By discussing with the experts in the form of structured interviews, we compiled a list of analytical tasks.
R.1 Epidemic Transmission Visualization: How do the citywide human trajectories distribute at a citywide level? How does the epidemic transmission process look? These visualizations help users better understand the epidemic situation of a big city from a perspective of human mobility.
R.2 Epidemic Control Policy: How to do the epidemic simulation by setting one specific policy (e.g., region lockdown, detection, telecommuting) or selecting several policies as a combination? These require our system not only to provide an easy-using frontend UI, but also to design a robust and flexible backend architecture for multi-policy simulation.
R.3 Spatiotemporal Setting: How to select a specific region to implement lockdown policy or telecommuting policy? How to set an infection detection point at a specific location? How to set the start date and the end date of one specific policy? User should be able to do these spatiotemporal settings with interactive visual assistance.
R.4 Basic Parameter Setting: How to set the basic parameters such as β 1 , β 2 , and r for the epidemic simulation model SEIR?
R.5 Advanced Parameter Setting: How to do the advanced parameter adjustments for the epidemic simulation model SEIR? For instance, human-to-human transmission probability r could vary from one type of POI to another. User should be able to adjust the transmission probability r according to POI distribution.
How to intuitively demonstrate and compare the evaluation results? User requests us to provide multiple visualization analytics results in a well-organized, userfriendly, and highly-informative layout.
EpiMob is a web application with frontend backend separation architecture. The frontend is implemented by React.js (for building user interfaces) and DECK.GL (for visual analysis of large-scale spatial data). The backend is designed as a Restful API, implemented by Python. A set of coupled modules are utilized to construct our EpiMob system, the architecture of which is depicted as Fig.2 analytics results are well displayed to help user compare different policies intuitively.
• The interactive module can specify: (1) the epidemic control policy such as "close region", "telecommuting (work-from-home)", or the combinations; (2) the spatiotemporal settings of the selected policy such as the specific polygonal area and the start/end data of policy implementation period; (3) the basic parameter settings including β 1 (the rate of transmission for the susceptible to infected), β 2 (the rate of transmission for the susceptible to exposed), and r (the number of contacts per person per day); (4) the advanced parameter setting like POI risk factor r POI . It is used to adjust the original r based on the POI distributions as the region containing more restaurants and bars is supposed to have a higher infectious risk. Here, (1) and (2) are combined as the human trajectories with specified restrictions. (3) and (4) are the basic and advanced parameters. Furthermore, user can set (1)∼(4) simultaneously as a combination of restriction policies.
• The query processing module can respond to the user settings on different restriction policies, also called as "queries", delivered by the interactive module. It first extracts the people who are affected by the given policy, then generates a substitution trajectory for each of those affected people.
• The simulation module can simulate the epidemic spreading with our trajectory-based SEIR model.
• The data preprocessing module can do data cleansing, interpolation, and indexing for citywide human mobility data and city POI data. LevelDB is used as the key-value database to efficiently store and retrieve trajectory data.
In this study, we used modified SEIR-equation to account for a dynamic Susceptible[S] and Exposed [E] population state, which was introduced by infectious disease experts Nanshan Zhong for predicting epidemics trend of COVID-19 [52] . The latent [E] population is asymptomatic but infectious, and [I] refers to the symptomatic and infectious population.
Here, we modified this model by replacing inflow/outflow rate with large-scale real GPS trajectory data, as Fig.3 . To construct a people flow for epidemic simulation from a raw GPS record dataset, in the first step, we need to discretize the time and coordinates. We selected 5 min as the time interval therefore divided one day into 288 time-slices. In addition, we meshed the city into hexagon mesh by H3 grid system [9] . The grid are generated by H3 Hexagonal mesh of Level 8. And we conducted the epidemic simulation in every hexagon mesh as time-slice increases, respectively. Our modified model is given by:
(1) Here, S(t) denotes the number of susceptible people in a hexagon mesh, N(t) denotes the total population, and E(t) denotes the number of exposed number. I(t) denotes the number of infected people. β 1 denotes the rate of transmission for the susceptible to infected, β 2 denotes the rate of transmission for the susceptible to exposed, and r(t) denotes the number of contacts per person per day, related to control policies. σ is the incubation rate which is the rate of latent individuals becoming symptomatic (average duration of incubation is 1/σ ), and γ is the average rate of recovery or death in infected populations. For basic epidemic parameter setting, we also set above parameter β 1 , β 2 , r(t), σ and γ as the estimated trends of COVID-19 (coronavirus disease 2019) transmission [52] . Basic epidemic parameter setting can be listed as follows: r = 15 as initial contact number per person per day, and r = 3 as the contact number of region-lockdown state. β 1 , β 2 , σ and γ are set as 0.15747, 0.78735, 0.154 (95% confidence interval) and 1/7 (incubation period of seven days).
When it comes to the restricted mobility model, we need extract the significant location places particularly home and work places to implement control policy. Most human activities are routine and people tend to spend time in the same places in their daily life. To extract the significant places particularly home and work places, we applied stay point extraction algorithm [35] based on the spatial and temporal values of points. We detected stay points for each individual in a trajectory of one month(from July 1st to July 31st, 2012). Stay points are detected when the individual spends at least one hour within a distance of 500 meters from a given trajectory point. Every stay points coordinates are the median latitude and longitude values of the points found within the specified distance. Finally, we compute the mesh id of these stay points' coordinates also according to level 8 of H3 grid system, which is used for getting mobile phone users home and work mesh to generate replacement-based restricted mobility model. By analyzing and classifying time duration of each mesh that corresponds to stay points of mobile user in the day of 24 − h period, home and work places can be possibly derived. We used periods from 00:00 to 06:00 for night time and 11:0017:00 for day time [48] . Some period was omitted due to the high possibility of being commuting time. Then, the percentage was calculated comparing the sum of all values in every mesh. Finally, we determine home and work places where mobile phone users spent more than 80% of their total stay time during the period of night and morning time, respectively. According to this standard, we select 11985 mobile phone users form 145507 users whose activities mainly located in Greater Tokyo area, in order to conduct epidemic simulation under different control policy. For example, stay hours detection of a mobile phone user who has determined home and work location in main stay mesh can be shown in Table 1 . 
Detection is a common control policy due to its flexibility and economy. However, where to set up detection point is a crucial problem for infection detection. At the same time, the setting of detection points is closely related to the distribution of POI. For example, government health management department often sets up detection points in public gathering areas such as subway stations or large shopping malls. As Fig.4 shows, users can set up reasonable trajectory-based detection points by exploring the distribution of concerned POI. And for proposed trajectory-based epidemic simulation under detection policy, after users select grid-based detection points (i.e. selected meshes), we assume that temperature detection is performed in the selected meshes in entire epidemic process, and the probability of detecting an infected person from the infected group is 87.9%, which is set according to the newest research of COVID-19 [19] . Once these infected persons are detected, they will be quarantined(i.e., cut off subsequent trajectories) and not infect others.
Telecommuting is a work arrangement in which employees do not commute or travel to a central place of work, such as an office building, warehouse, or store. In this system, we try to simulate the spread of infectious diseases under telecommuting restriction from the view of GPS trajectory. And this government control policy often relates to certain administrative district. By analyzing activity pattern of mobile phone users' GPS trajectory, we can acquire home and workplaces of mobile phone users and identify their workplaces belonging to which city or prefecture in Greater Tokyo area, and we can detect how many people work in every city or prefecture in Greater Tokyo area as well. Therefore, our system allows users to select administrative districts where people stay at home and work remotely, and users can set the telecommuting ratio of selected administrative districts. For proposed epidemic simulation under telecommuting restriction policy, we randomly select mobile phone users in selected administrative districts, and the number of selected users meets user-defined telecommuting ratio. We detect selected mobile phone users' grid-trajectory of one month, and determine if they go to work mesh day by day. And we combine their work days with the period of policy implementation to replace the grid-trajectory of working day with home mesh during the period of policy implementation, i.e. making selected users stay at home all day during influenced work days.
Region lockdown is a very urgent infectious disease control policy, which may bring huge loses to the society and economy. On 23 January 2020, China imposed a lockdown in Wuhan and other cities in Hubei province in an effort to quarantine the center of an outbreak of COVID-19. Aside from locking down the Greater Wuhan area, Hubei residents were dissuaded from returning to their workplace. The effectiveness and necessity of such undertakings have been proved. For example, Wu et al. [49] , predicted that without control measures the epidemic size in Wuhan would reach 75,000 infections by January 25 and the epidemic would peak in April. Similarly, Read et al. [38] , predicted a peak of 190,000 cases by February 4 without control measures. For proposed epidemic stimulation under region lockdown, initially, our system allows users to circle polygons of any shapes as a blocked area. So we can got all the mesh numbers within the closed area based on H3 grid system. As is shown as query processing module of Fig.2 , once users determine the blocked area and blocked time period, the affected mobile phone userss trajectory simulation can be divided into following two situations. For mobile phone users who stayed in the blocked area at the beginning of the blocked time period, their gridtrajectory remained unchanged throughout the blocked period. And for those mobile phone users who visited the blocked area after the region lockdown, we query their one-month historical trajectory database, and randomly find the trajectories that have not passed the blocked area for a day to replace the trajectories that passed the blocked area that day for every mobile phone user. Noted that we set r = 3 as epidemic parameter in the blocked area, which denotes the number of contacts per person per day.
In this section, we present the design goals from the perspective of user requirements (6.1). Then introduce in detail the visualization views of EpiMob for interactive policy setting and results analysis (6.2,6.3,6.4).
G1: Flexible basic parameters settings of the propagation model. The living habits, living environment, and public health conditions of different cities are different, which leads to the variation of β 1 , β 2 , r.
The system should allow the user to set the parameters of spread based on the objective condition of the target city. Besides, the traditional spread model treats the whole city as a homogeneous region, which means the spreading parameters are all the same across the whole city. However, depending on the functional division of the city, some regions have more entertainment facilities/shopping malls than others like the central business district. It makes people more likely to be exposed to other people and causes a higher r value. To address this issue, the design should support a more fine-grained setting(i.e., each grid has its own r value). G2: Interactive spatial-temporal restriction setting. A specific restriction policy must have concrete spatio-temporal information(i.e., the implementation period and regions). However, the setting of spatialtemporal attributes is quite complicated for users due to the vast selection space. From the perspective of users, they want to set time range and regions reasonably, intuitively, and conveniently. To satisfy this requirement, we need to provide some prior knowledge to assist the user setting, and the prior knowledge should be displayed intuitively. Besides, users can preview, adjust their settings before submitting to the simulation module. G3: Comparative visual analysis of different control policies. After submitting different policies, it is inevitable to compare the advantages and disadvantages of different policies. However, due to the diversity of potential geographical selection space, how to help users distinguish different policies has also become a challenge. For example, A user launched two policies, both including a variety of regions, and the two regions set intersect a lot. It is hard to automatically generate a name code for them so that they can be easily distinguished. In order to facilitate comparison, our interactive design also needs to boot and allow users to set a name code for policy by themselves. Further, with the help of distinguished name codes, we also need to support users to select different policies for comparison comfortably and save the results for further analysis.
Users are desired to set basic epidemic parameters and POI risk to conduct trajectory-based epidemic simulation and acquire the solution views for the infectious results.
Different cities have different actual conditions. As shown in the Fig.1 -A4, we allow experts to set the basic spread parameters(i.e.,β 1 ,β 2 ,r) based on the concrete situation. Also, the selection of simulation periods is supported, which could help experts to explore the impact of periodical human behavior changes on epidemic control(e.g., the human mobility behavior in winter and summer is quite different [54] ).
In order to achieve the design objectives mentioned in G1, we designed the POI Risk Adjustment panel to reduce the difficulty of fine-grained r setting( Fig.1-A5) , which utilizes the POI information in a grid to set its r value. As there are many kinds of POI scattered in a grid, our plain idea is that experts could assign a new r value to each kind of POI based on their experience. The specific setting method is to adjust the r-value change rate of each POI type based on the r base value, also called risk adjustment in EpiMob. Then, according to the proportion of each type of POI in the grid, weighted summation to calculate a new r value (r new ). The concrete calculation method of r new for each kind of POI is shown in Equation (2).
Users can obtain sufficient and effective prior knowledge such as traffic flow and POI distribution through interactive restriction setting view to formulate control policy that meets users' expectations. To help users discover potential detection points, we design a detection view, which shows the geographic distribution of various types of POIs (Fig.4) . In actual life, most of the detection points set at the entrance and exit of POI, such as the entrances and exits of stations and large shopping malls. The user may prefer to select the locations where some kinds of POIs are denser than others(e.g., In Fig.4 the user selects the places which have a higher entertainment POIs density than others). In this view, users can tick one or several types of POIs to observe the distribution.The method of adding detection points is straightforward. We supply two types of adding methods in the detection control panel ( Fig.1-A2) : draw selection areas directly on the map or drag mark to the location of interest. After successfully added, a mark will be generated at the selected grid, indicating that the detection will be performed here. In the subsequent simulation, all passing people will be detected according to the detection model in Section 5.2.1.
To help the user discover areas which administrative district implement telecommuting policy is necessary, we design the telecommuting view as Fig.1-A3 shows. Users could set a series of regions to execute telecommuting. According to the region's conditions, users can control the policy executive strength by setting the start date, reduction rate, and duration ( e.g., Reduction to 90% means that 90% of people work in that region will work at home). To supply more prior knowledge for the region selection, we integrate a heat map of all person's workplaces on this view (Fig.5) , when the mouse places over an area, the information of the area is displayed. Users could select the regions where has a larger daily commuting flow to reduce the spread risk. The switch locates on the right up corner of the telecommuting panel sets the visibility of heatmap. Fig. 5 : Workplace Heatmap. The darker color represents more people working at there.
In order to help users select potential lockdown areas, we propose the region lockdown view, which provides the traffic flow information of the city. Fig.1-A1 shows the control panel of this view, where users could set the lockdown start date and duration. By opening the switch on the control panel, users could get the prior traffic flow information ( Fig.1-A6) . Generally speaking, a large-scale epidemic spread has more possibility to happen at the place with heavy traffic flow. We map the flow value to a color schema(i.e., dark blue to dark red) in which the deeper color represents the larger flow (for each grid, the traffic flow refers to the number of move in and move out trips during a period). Besides, we provide two auxiliary subviews containing more detailed information. Flow Delta sub-view: users can get the flow change information, which is calculated based on the data of the same period last week. this sub-view also can help to explore abnormal flow. For example, in Fig.6 , we find a significant event, the Sumida River Firework Festival. Further, based on the area where a large amount of abnormal traffic found, the user can block the area during the abnormal period, perform a customized propagation simulation, and analyze the impact of stopping the large-scale activity on the spread of the virus. OD Analysis sub-view: users could analyze the in-outflow distribution of the target area on the map by this one. With the above prior knowledge supplied in our region lockdown view, users could find potential blocked areas effectively.
Users can acquire the policy results according to their basic epidemic parameter setting and the selected control policy, including not only single policy result view, but also the comparative analysis view. Single Policy Result View. After the user launches a mobility restriction policy, the result of that policy will be displayed in the policy results overview panel( Fig.1-B ). Fig.7 shows a policy result, named "lockdown tokyo center from 0708", referring to perform lockdown in Tokyo center part since July 8th. As mentioned in G3, in order to facilitate subsequent comparisons, the policy name is set by the users. The clips under title represent a preview of the basic settings, which could deliver an intuitive message of the policy. In the chart section, the blue curve represents the cumulative number of infections, and the purple area represents the 95% confidence interval. When the mouse hovers on the corresponding position of the curve, specific details of that position will be displayed. Besides, there is a checkbox in the upper right corner of view, which designed for users to conduct comparative analysis conveniently. The user checks the target policies first, then clicks the compare button (the bottom right corner of Fig.1-B) , and the corresponding analysis result will be displayed in the Comparative Analysis View. Comparative Analysis View. After the user selects several single policies to compare, a new comparative view will be generated, which will put multiple curves together for comparative analysis (Fig.1-C) . Similarly, the user can customize the name of the analysis result.
In this section, we conducted several case studies to validate proposed trajectory-based epidemic model and EpiMob system. We first analyzed the epidemic simulation of large public events to verify if our proposed trajectory-based epidemic simulation can actually reflect the spread of infectious disease. Then we explored the containment of infectious diseases under different control policy, i.e., detection, telecommuting and region lockdown. Furthermore, we also explored the effect of multipolicy combination for epidemic spread. Finally, our EpiMob system is evaluated by the experts in the fields of immunology, computation engineering and urban computing. 
Stopping large public events including sports fixtures and concerts plays a crucial role in curbing the spread of infectious diseases. In this scenario, we aim to verify our system by doing the epidemic simulation on a public gathering event, namely Japanese Sumida River Firework Festival. It is a firework festival with a long history, being a successor to the "Ryogoku Kawabiraki Firework" festival that began in 1733, and it is a signature Tokyo summer event enjoyed by many Japanese people. First we detect stay points of GPS trajectory of mobile phone users to determine if user attended the Japanese Sumida River Firework Festival in Taito Ward of Tokyo during the period from 19:00 to 21:00 on July 28th, 2012. Then we extract 1319 users from raw GPS log dataset. As Fig.8(a) and Fig.8(b) show, we can clearly observe that mobile phone users who attend Firework Festival gathered around Sumida River at 20:00 PM, on July 28th, 2012. And people had dispersed to leave from the Sumida River Firework Festival at 23:00 PM. Furthermore, we conducted trajectory-based epidemic simulation for these people who attended the Firework Festival on July 28th. We randomly select 10 people as initial infected persons, as Fig.8(c) shows, OD from their last stay point to Sumida River of overall crowd who attended the Firework Festival, red OD lines among them denote that initial infected persons attend this festival. The epidemic result can be shown in Fig.9 , the curve Increasing infected number per hour on July 28th obviously rises from 17:00 PM when the crowd started to gather, and the increasing number declines as the Firework Festival ended. And we can find the spread of infection by the crowds after the event whose OD from Sumida river to next stay points can spread the virus to other places in Fig.8(d) . These analysis results prove our proposed trajectory-based simulation can truthfully reveal the cluster spread of infectious diseases, and dangerous consequences of the spread of viruses caused by large public events.
This case is aimed to demonstrate the effectiveness of the spread of infectious disease under different control policy based on proposed trajectory-based epidemic simulation. We apply 11985 mobile users' trajectory of one month (from July 1st to July 31st, 2012) as experimental GPS trajectory dataset. In order to ensure the validity of the system solutions of epidemic simulation under different control policy, we applied MCMC (Markov Chain Monte Carlo) to conduct repeat random sampling for initial random 10 infected people, and we also drew the 95% CI (confidence interval) for the simulation results in the solution view. Noted that we applied parallel computing for the above sampling to ensure computational efficiency. Finally, all of the simulation results will be reviewed by domain experts. Detection. The experts can easily find the location of desired detection point according to the distribution of various POIs on the map by detection view (Interactive Detection Station Placement) of EpiMob. The experts set up detection points in the clusters of entertainment, supermarket and public place, respectively, and compare their effectiveness of the spread of infectious diseases. As a result, the experts also can easily acquire the result of epidemic simulation ( Fig.10-A2 ) under different distribution of detection points (Fig.10-A1) . We can find that setting up temperature detection point in public places don't have obvious effects than entertainment and supermarket. Telecommuting. Also, the experts can easily view heat maps of workplaces in various cities or prefectures in Greater Tokyo area by telecommuting view (Workplace Distribution) of system. As observed in Fig.10 -B Solution View, the experts acquired the solution for implementing telecommuting at different telecommuting ratios in Tokyo. And the experts can conclude that telecommuting policy is very effective in the early stages of the spread of infectious disease, and higher telecommuting ratio is more effective, which is in line with the true expectations of this policy. However, in the middle and late stages of the spreading, the proportion of telecommuting has little effect on the final results. Region Lockdown. With the help of region-lockdown view, which provides the traffic flow information of the city including flow delta sub-view and OD-analysis sub-view, the experts can easily find the potential region-lockdown area by these sufficient prior knowledge. As observed in Fig.10 -C Solution View, the results of epidemic simulation under region lockdown also coincides with the projections of the expert. The sooner the closure policy is implemented, the better the spread of the epidemic can be effectively controlled.
Multi-policy Comparison. The experts finally conduct a multi-policy comparison that not only a certain one policy is implemented and analyzed, in order to find a relatively optimal solution to control the spread of epidemic. As compared in Fig.10 -D Solution View, the experts compare five strategies under different control policy or their combination. These control policy are telecommuting (From July 8th, 90% of telecommuting ratio), region lockdown (From July 8th), the combination of telecommuting (From July 8th, 90% of telecommuting ratio) and region lockdown (From July 8th), the combination of telecommuting (From July 8th, 90% of telecommuting ratio) and detection (Set up detection point in the cluster of entertainment), detection (Set up detection points in the cluster of entertainment), respectively. According to these infectious results of five strategies, the experts think it's a very interesting and reasonable finding that the detection in the cluster of entertainment works better than any other.
Epidemic simulation and control policy analysis is a multidisciplinary research problem that involves immunology, computation engineering, and urban computing. Therefore, we ask three experts in those corresponding domains to evaluate our EpiMob system. Specifically, the first (EA) is an expert in pathogenic microbiology and immunology, the second (EB) is an expert of high performance computing, and the third (EC) is a senior researcher in urban computing. Reliability of Epidemic Simulation and Policy Evaluation. EA confirmed that our trajectory-based epidemic model is based on a modified SEIR equation with dynamic susceptible and exposed population as variables proposed in [52] . EA commented, "this epidemic model utilizes real GPS record data to conduct epidemic simulation, which can be used for small sites, such as homes, workplaces, and a specific gathering. Based on this, the corresponding policies and regulations can be formulated, and the action tracking (individual trajectory) can be used to set up detection points, remote offices, and city blockades. And this system allows for an intuitive preview and a comparative analysis of the selected strategies. Moreover, the system can assess the impact of a combination of multiple strategies (i.e. detection, telecommuting and region lockdown) on the spread of infectious diseases." However, he mentioned that it would be better if this system could further unseal and predict the likely risks of travel.
Visual Design and Usability. The experts confirmed that our EpiMob system has a clear and friendly UI, which provides rich interactions to conduct reasonable settings for epidemic simulation. EB praised the easy interactions, and thought that it's easy for normal people to understand the spread of infectious disease and the government control policy. At the same time, EB confirmed the strategy including parallel computing and MCMC (Markov Chain Monte Carlo) sampling improved the computation efficiency, and could bring a credible result. However, he mentioned that this system need apply distributed computation framework to simulate more population in the future. Rationality of Restricted Human Mobility Model. EC confirmed that human mobility is highly related to the spread of epidemic, and trajectory-based epidemic model is a very good and interesting application by building connection between human mobility and epidemics. EC commented, "the replacement-based restricted mobility model is very promising in simulating the restricted human mobility under different policies. This is a relatively underexplored but highly challenging direction in the urban computing community. In particular, public policy is quite complex and multifaceted, so visual interaction for human mobility simulation under public policy is very necessary and reasonable. Their interaction design for human mobility and epidemic simulation complements the current most human mobility studies in the sense of receiving more complex and in-time input from users as well as visualizing key information for decision making."
In this study, we design an interactive visual analytics system called EpiMob to effectively measure and evaluate different human mobility restrictions (i.e., detection, telecommuting, region lockdown) for epidemic control. First, a novel trajectory-based SEIR model is proposed to simulate the epidemic spreading based on real-world human mobility data and city POI data. Then we design a "trajectory replacement" strategy to generate a new set of human trajectories according to the mobility restrictions. The new generated trajectories will be fed into our trajectory-based SEIR model to trigger a new round of simulation. Through EpiMob, user can easily select one policy or a combination of policies as the simulation target and set the spatiotemporal settings as well as the epidemic parameter settings with interactive visual assistance. By employing the advanced visualization techniques, those simulation results could be confirmed and compared in a well-organized, user-friendly, and highly-informative layout. The functionality and usability of our system are validated through multiple case studies and domain-expert interviews. In the future, we will continue to improve our system from the following aspects: (1) integrating more epidemic control policies and the interactive parameter settings;
(2) enhancing the trajectory processing capability for bigger trajectory data;
(3) modifying the user interface for better user experience.