Agent-Based Campus Novel Coronavirus Infection and Control Simulation
Pei Lv, Quan Zhang, Boya Xu, Ran Feng, Chaochao Li, Junxiao Xue, Bing Zhou, Mingliang Xu
11 Agent-Based Campus Novel Coronavirus Infectionand Control Simulation
Pei Lv, Quan Zhang, Boya Xu, Ran Feng, ChaoChao Li, Junxiao Xue, Bing Zhou,and Mingliang Xu,
Member, IEEE
Abstract —Corona Virus Disease 2019 (COVID-19), due to itsextremely high infectivity, has been spreading rapidly around theworld and brought huge influence to socioeconomic developmentas well as people’s production and life. Taking for example thevirus transmission that may occur after college students return toschool during the outbreak, we analyze the quantitative influenceof the key factors on the virus spread, including crowd densityand self-protection. One Campus Virus Infection and ControlSimulation model (CVICS) of the novel coronavirus is designedin this paper, based on the characteristics of repeated contact andstrong mobility of crowd in the closed environment. Specifically,we build an agent-based infection model, introduce the meanfield theory to calculate the probability of virus transmission,and micro-simulate the daily prevalence of infection amongindividuals. The simulation experiment results show that theproposed model in this paper fully illuminate how the virusspread in the dense crowd. Furthermore, preventive and controlmeasures such as self-protection, crowd decentralization andquarantine during the epidemic can effectively delay the arrivalof infection peak and reduce the prevalence, and thus lowerthe risk of COVID-19 transmission after the students return toschool.
Index Terms —Infection model, Crowd simulation, Agent-basedsimulation, Epidemic prevention and control.
I. I
NTRODUCTION A T the end of 2019, the pneumonia epidemic caused bynovel coronavirus swept the world, bringing varying de-grees of impact on the economy, production, life, etc [1]. Thevirus spreads rapidly and widely, especially in the environmentwith high crowd density and strong crowd mobility. In re-sponse to the situations, China took various counter-measuresimmediately, such as extending citizen holidays, postponingthe return to work and school, and assisting the disaster areas,which effectively reduce the impact of the spread of the virus.To tackle the problem of suspend classes, governments aroundthe world proposed various distance learning programs throughmodern technologies to guarantee students to continue theireducation. However, due to the unsatisfactory teaching effect,it is very important to return to school. Several common waysof prevention on campus are shown in Figure 1. As a relativelyspecial group, colleges students spread all over the country,and will contact with a large number of people on the way back
Pei Lv, Quan zhang, Boya Xu, Ran Feng, Chaochao Li, BingZhou and Mingliang Xu are with the School of Information En-gineering, Zhengzhou University, Zhengzhou 450001, China (E-mail:[email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]. cn; [email protected]). Junxiao Xue is with the School of Software, ZhengzhouUniversity, Zhengzhou 450001, China (E-mail: [email protected].) (a) Keep distances (b) Physical examinationFig. 1. Some of campus prevention and control measures. to school. After return to school, students will inevitably gathertogether to study and live. The above conditions will have anegative impact on the epidemic prevention and control work,and the large gatherings of dense crowd with strong mobilitywill even accelerate spread of the epidemic [2]. Therefore,how to manage the college students after they return to schoolis a significant problem to be solved.Regarding the spread of novel coronavirus, we can ana-lyze their laws and trends by constructing infection models.In most of existing models, SIR model and SEIR model,which are based on the dynamic systems [3], are adoptedto fit the urban infection curve. However, it is a completelydifferent problem on campus. The university is a relativelyclosed space, where a lot of contact is unavoidable [4]. Theaverage number of people contacted each day on campusis different from that of urban residents. The existing urbansimulation model cannot be applied to the university environ-ment. Besides, novel coronavirus is quite different from otherprevious infectious diseases. For example, SARS and anotherinfamous coronavirus, which broke out in 2003, researchershave also built models to study its infectious characteristics.Although the incidence characteristics and other aspects ofSARS are relatively similar to COVID-19, SARS dose nothave infectiousness in the latent period, which is differentfrom the present one. Therefore, we cannot reuse the previousinfection models. Moreover, the existing simulation models forlarge scale population are usually macroscopic, which meansthat they do not focus on individuals, hence cannot reflectthe differences among individuals. The microscopic simulationmodel requires consideration of attributes of each individualin detail. As the number of individuals studied increases, thecalculation time increases significantly. As the virus spreadrapidly and widely, The simulation time is the key factor toevaluate the model.In response to the outbreak of coronavirus, governmentsaround the world have took various measures to lower the a r X i v : . [ c s . S I] F e b influence. For example, China has developed a series ofcontainment and obtained satisfying results. To be specific,the Chinese government approved the travel ban, encouragedpeople to stay at home to avoid gathering, restricted social ac-tivities, etc. However, some countries or organizations ignorethe spread effect of the virus in the dense crowd, aggravatingthe situation. A case in point is "Diamond Princess", where thevirus spread rapidly due to insufficient preventive and controlmeasures in the early stage. Taking a lesson from it, it isnecessary to take strict measures to curb the spread of thevirus in the environment with high-density population [5].In this paper, we comprehensively consider various factorsthat cause the spread of the disease, and propose a campusvirus infection and control simulation (CVICS) model of thenovel coronavirus, based on the characteristics of repeatedcontact and strong mobility of crowd in the closed envi-ronment. The agent is the main components in simulation,and each individual can sense the surrounding environmentindependently [6]. The movements of the individual are givenby social force [7][8]. At the same time, the spread of thevirus among individuals in different scenes on campus can besimulated. The advantage of this model is that it can presentthe state information of each agent in the environment ateach moment from a micro perspective, making the simulationmore realistic. Takinge comprehensively consider the keyfactors such as crowd density and self-protection into account,effective preventive and control measures such as travellingin batches, staggered travel and isolation are put forward.According to several groups of comparative experiments,we can observe the trend of virus transmission on campus.Through the intervention of group behavior, the infection ratewas effectively reduced.Our major contributions are listed as follows:1. We propose a simulation model (CVICS) of the novelcoronavirus, based on the characteristics of repeated contactand strong mobility of crowd in the closed environment.We simulate the daily prevalence of infection among collegestudents, and propose effective control measures with analysis.2. Considering the differences among individuals, we designan agent-based simulation, introduce the mean field theoryto calculate the probability of virus transmission, and micro-simulate the daily prevalence of infection among individuals.3. Taking Zhengzhou University as an example, we simulatethe virus infection among college students during the epidemicperiod. Then we propose control measures such as travellingin batches, staggered shifts and isolation, and prove theireffectiveness on reducing the infection rate.II. R ELATED WORK
In this section, we briefly introduce the infection model andcrowd simulation model.
A. Infection model
Nowadays, the spread of virus is generally studied byconstructing various infection models, to carry out an accuraterisk assessment. In the micro model, the classic SIR model divides the population into susceptible, infected, and recover-ing groups [9]. It is a good demonstration of the process ofinfectious diseases from the onset to the end. The premise ofusing this model is that patients suffering from such infectiousdiseases can recover, and can produce permanent antibodies,and no longer participate in the spread of the disease. Sincethe model can well simulate the propagation of other media,it has also been widely applied to other fields. As the typesof infectious diseases become more complex, the model ofinfectious disease is constantly improved. If the infectiousdiseases studied have an incubation period, the improved SEIRmodel based on the SIR model will be generally used. Themodel divides the population into susceptible, latent, infectedand rehabilitated, which can describe the transmission processof the epidemic more accurately. When the SARS epidemicbroke out in 2003, most of the SIR or SEIR models were usedto fitting the infection curve of the city. Liang [10] conductedexperiments through the establishment of a propagetion growthmodel by cbnsidering the growth rate as well as the inhibitionconstant of infectious diseases, which showed that the infec-tion rate and its changes over time are the most importantfactors affecting the spread of SARS. In addition, there areother similar models such as SI [11] and SIRS [12]. Shi etal. [13] produced an epidemic dynamics model through thestudy of infectious models. In the study of infectious diseases,researchers not only predict the number of people in variousstages of disease, but also need to consider the causes ofdisease, transmission media, other relevant social factors andso on [14]. It can help decision-makers formulate preventionand emergency plans to prevent further deterioration of thevirus spread.When exploring the infection situation of colleges anduniversities, the state of recovery is not considered. Oncethe suspected cases are found, they are sent to the schoolhospital for isolation and then transferred out of the college toa designated location for treatment. Different from the mostcommonly used models such as SIR and SEIR to calculate thetrend of the number of people in each state under the epidemic,campus infection simulation focuses on suspected groups thatmay be infected and focuses on preventing the large spread ofthe virus. Currently, the most commonly used models are notcompletely suitable for studying epidemics in universities.
B. Crowd simulation
The technology of crowd simulation has been widely usedin many fields. It can not only be used for the agents tofill the virtual environment to generate the simulation ani-mation of the group state [15], but also be regarded as animportant way to design architectural plane and evaluationcost [16][17]. Common crowd simulation models include rule-based models, cellular automata models, social forces-basedmodels [18] and agent-based models [19]. Among them, agent-based simulation has attracted the attention of most researchersdue to its self-adaptive interaction with the environment in acomplex sences. In recent years, More and more researcherspay attention to the simulation model of infectious diseases.Kleczkowski et al. [20] uses the cellular automata model,
Fig. 2. The system overview of our work. Agent model, infection model and environment model are established for crowd simulation in campus. In theprocess of simulation, the virus spreads while the agent is active in the environment. At the same time, various control measures are taken according to thesimulation results. that is a typical microcosmic model. The simulation modelstudied the impact of relevant information in the local spaceon the spread of epidemics. Eubank et al. [21] developed anagent-based epidemic simulation system called EpiSimdemics.Barrett et al. [22] developed EpiSimdemics based on the workof Eubank et al. A scalable parallel algorithm is proposedto simulate the spread of infection in a large-scale socialnetwork in reality. Bissett et al. [23] describes an integratedmethod for computational health informatics, which includesindividual-based population construction and agent-based dy-namic modeling. At present, there is still a challenge for large-scale crowd simulation. The macro crowd simulation modelusually studies the whole and ignores the heterogeneity amongindividuals. The micro crowd simulation model focuses on asingle individual, but when the number of people is huge, alarge amount of information needs to be calculated, and itis difficult to guarantee the speed and quality of calculationat the same time. Yang et al. [24] introduce the mean-fieldtheory to calculate the crowd movement, which formulatethe multidimensional problem into two-dimensional problemto reduce the computational complexity. It can better handlelarge-scale crowd movement simulation problems.Our model uses a agent-based simulation by the social forcemodel to describe microscopic individuals. The social forcemodel can vividly describe the impact of the surroundingenvironment (such as other individuals and obstacles) on thepedestrian behavior, and can realistically simulate the dailybehavior of students on campus, which is not available insimulation systems such as EpiSimdemics. By observing theimpact of the interaction between people in different scenarios(classrooms, restaurants, dormitories, etc.) on the spread ofthe virus, corresponding measures can be taken to reduce thespread of the virus.III. C
AMPUS VIRUS INFECTION AND CONTROLSIMULATION
Our model is to study the infection situation of college stu-dents to implement effective management and control studentsof colleges and universities. We take Zhengzhou University asan example. This university is located in the Central Plains ofChina, with a wide distribution of students, and the campusenvironment is very representative.
TABLE IW
ALKING PATHS
Walking PathsCategory 1 dormitory → teaching building / library → restaurant → teaching building / library → dormitoryCategory 2 dormitory → teaching building / laboratory → restau-rant → teaching building / laboratory → dormitoryCategory 3 dormitory → laboratory → restaurant → laboratory → dormitoryCategory 4 dormitory → administration building / library → restau-rant → administration building / library → dormitory The agent-based model is used to simulate the populationinfection situation on the campus of Zhengzhou Universityduring the epidemic without control measures and after thesemeasures are taken, to better manage college students. In thisway, we can ensure students’ learning quality while preventingthe spread of the virus, and reduce the number of infectedpeople on campus as far as possible.The system overview is shown in Figure 2.
A. Agent definition
Students in different majors have different learning tasks,so they are divided into four categories according to theirmajors. In the epidemic environment, each student needs totravel in accordance with the regulations to try to avoidcross-infection among different groups as shown in Table I.Everyone starts from the dormitory, visits their respectivebuildings, and returns to the dormitory. According to the Dijk-stra [25] algorithm, the shortest route between two destinationsis obtained. In the simulation, the students walk along theestablished path. The walking speed of the people is evenlydistributed in the interval of . 𝑚 / 𝑠 ∼ . 𝑚 / 𝑠 [26].According to the individual infection status, the studentsare divided into three categories: susceptible, latent, andinfected. We set a metric 𝑃 _ inf for the agent to calculatethe probability that the agent may be infected, to determinethe infection status. Within a certain range, if the measurereaches the threshold 𝑇 ( 𝑇 = ), it means that the individual isin an infected state at the moment, and the infection statehas changed from a susceptible person to a person in the TABLE IIP
ROPERTIES OF AGENTS
Properties Descriptiongeneral information genderagegeneral state movevisitrestmovement state moving speedimmediate locationvisit state teaching buildingclassroomseatrest state dormitory buildingdorm roominfection state probability of infectiondays of infectionsusceptible, latent, infected latent period. After 7 days, people in the incubation periodwill be transformed into confirmed patient. According tothe transmission characteristics of the novel coronavirus, allstudents in school are likely to be infected with the virus, andindividuals are infectious during the incubation period andthe onset period. According to the latest research, the basicreproduction number (R0) value is as high as 5.7. This meansthat it is extremely disseminated and infectious, individuals ina latent state and an infected state are infectious [27].In order to simulate the spread of the virus more realisti-cally, the general state, movement state, visit state, infectionstate and other attributes are added to each agent, as shown inTable II.
B. Agent-based novel coronavirus infection modeling
To construct a population infection model for colleges anduniversities, the infection distance is one of the importantfactors, in other words, the range of the virus that can spread.We set this parameter to 𝑚 [28], that is, the virus carrier canaffect other individuals less than 𝑚 away from it. At the sametime, the number of days the virus is carried in the humanbody may have an impact on the spread of the virus. It isreported that the incubation period of COVID-19 is generally3 to 22 days, and the experiment is set to 7 days [29]. Due tothe incubation period, virus are also contagious. We considerthat as the number of days of carrying the virus in the humanbody increases, the infectivity increases linearly. The influenceof the number of days a virus carrier carries the virus on theinfectivity of the virus is calculated by the formula (1): 𝑓 (cid:0) 𝑖 𝑑𝑎𝑦 (cid:1) = min ( 𝑖 𝑑𝑎𝑦 / 𝐼 𝑝𝑒𝑟 , (cid:1) (1)where 𝑖 𝑑𝑎𝑦 indicates the days of carrying the virus; 𝐼 𝑝𝑒𝑟 = means that the incubation period is 7 days, and the infectiousperformance increases linearly with the increase of the numberof days the virus incubates in the body. When the virusis carried for 7 days or more, the infectivity is no longerenhanced.We consider the influence of the distance between theindividual and the person in the incubation period on the spread of the virus. The influence of the physical distanceis expressed by formula (2): 𝑓 ( 𝑑 𝑛 ) = (cid:26) 𝑅 √ 𝑅 − 𝑑 < 𝑑 < = 𝑅 𝑑 > 𝑅 (2)where 𝑅 represents the radius of infection and the value setto 𝑚 . When individual distances 𝑑 < = 𝑅 , the greater thedistance, the smaller the probability of virus transmission.When the distance 𝑑 between individuals exceeds 𝑅 , theprobability of individual infection is not affected by the virus.Air humidity, temperature, inhaled air concentration, themutual distance between individuals and other factors may alsohave an impact on whether a susceptible person is infectedwith the virus [30]. The combination of these factors byother individuals within the individual’s perception range willgenerate an infection probability for the central individual. Togenerate an infection probability separately, it will be verycumbersome to calculate the influence of these factors onthe individual if other individuals in the perception range arecalculated separately.Therefore, we use the mean field theory to calculate theprobability that an individual may be infected with the virus.It comprehensively calculates the impact of all individuals,which can greatly simplify the complexity of the calculation.Specifically, We divide the number of days patients carry thevirus into 8 time periods. They respectively indicate that novirus carried, carrying the virus for 1 day, and increasing tocarry the virus for 7 days or more. The individual infectionprobability formula is as follows: 𝑃 _ inf = ( 𝛽 ) ∑︁ 𝑖 = 𝑁 𝑁 ∑︁ 𝑛 = 𝑇 𝑗𝑛 𝑓 (cid:0) 𝑖 𝑑𝑎𝑦 (cid:1) 𝑓 ( 𝑑 𝑛 ) (3)where 𝑁 means that there are 𝑁 other individuals in theperception range of central body; 𝑇 𝑗𝑛 indicates that the 𝑛 thperson carried the virus for 𝑗 days. The probability distributionis obtained by dividing the number of people in each period bythe total number of people; 𝑁 (cid:205) 𝑁𝑛 = 𝑇 𝑗𝑛 indicates the proportionof people in each period; 𝑑 𝑛 represents the distance betweentwo individuals; 𝛽 represents the group protection rate. In otherword, the proportion of the number of people who take self-protection in all groups.The day is divided into different time slices, and theindividual’s infection probability is continuously updated withthe time slices. During the simulation process, the systemcalculate the infection rate of one time slice and the next timeslice, and take the maximum value of them. At the end of theday, the random value will be given by uniform distribution.If the value is within the individual’s infection probabilityinterval, it means that the individual will be infected. C. Simulation environment modeling
Generally colleges and universities occupy a large area andthe roads on the campus are intricate. To meet and manage thedaily activities of teachers and students during the epidemic,teachers and students will be prohibited from entering andleaving the campus at will. The campus will be dividedinto different functional areas, and each area will have an
Fig. 3. The distribution map of buildings. Different colors represent variousfunctional areas.Fig. 4. The map of road network. The orange line represents the road andthe green dot represents the node. entrance. The crowd is only allowed to enter and exit fromthis port, in order to prevent the spread of viruses caused bythe random shuttle of teachers and students in the campus.The buildings in the same functional area are combined asa whole. The winding roads are closed and not passable, asshown in Figure 3As shown in Figure 4, the road network can often berepresented by an undirected graph. The nodes in the figurerepresent road break points and intersections in the road net-work. The line segment connected by two nodes in the figureincludes attributes such as length and width. These attributescan describe the detailed information of each path in the mapand the topology information between the paths clearly. Underepidemic control, students strictly abide by school regulationsand start from their location to their destination within thepermitted time. It is represented by a route in the figure, andthe route has no closed loop. Starting from the dormitory andreaching the destination along the route, each student whomoves has a specific route. Students in the same dormitorybuilding have the same starting point and are divided on theway, and all routes have no closed loop. In the process ofstudents moving from dormitory building to other areas, thestarting point is taken as the root node, the midway road nodeis taken as the child node, and the destination is taken as theleaf node. A multi-branch tree with the dormitory building asthe root node will be formed, as shown in Figure 5.The multi-branch tree can be used to record the topologicalinformation of each required road segment, and the attributeinformation of the road segment is described by the nodeattributes. The
𝐿𝑒𝑛𝑔𝑡ℎ attribute in Table III not only includes
Fig. 5. The classification of the nodes in road network.TABLE III T OPOLOGICAL PROPERTIES OF THE ROAD SECTIONS
Attributes DescriptionParentsNode The parent node of this road node.ChildrenNode All children nodes of this road node.Length(m) The length of the path is represented by thisnode to its parent node.Width(m) The width of the path from this node to its parentnode.Weight The total number of people passing by this node(percentage of total people). the length of the path itself, but also the distance from theroot node to this node. For example, the distance from anode to its parent node is . 𝑚 , and the distance to its rootnode is . 𝑚 . The 𝑊 𝑒𝑖𝑔ℎ𝑡 attribute is a sequence, whichcontains the time when the crowd passes this road node andthe corresponding number of the crowd, such as the valueof the weight attribute is <300,600,0.05>. About of thetotal number of students will pass through this node between 𝑠 and 𝑠 . The time interval of crowd passing throughthe node is inversely proportional to the width of the road.According to the weight attribute, the crowd density of anyroad node can be estimated at a certain moment. The timethe crowd passes through the road node can be expressed bythe following formula: 𝑡 𝑖 𝑠𝑡𝑎𝑟𝑡 = 𝑙 𝑖,𝑡𝑎𝑡𝑎𝑙 / 𝑣 𝑚𝑎𝑥 𝑡 𝑖 𝑒𝑛𝑑 = 𝑙 𝑖,𝑡𝑎𝑡𝑎𝑙 / 𝑣 𝑚𝑖𝑛 Δ 𝑡 (cid:48) 𝑖 = 𝑡 𝑖 𝑒𝑛𝑑 − 𝑡 𝑖 𝑠𝑡𝑎𝑟𝑡 (4)where 𝑡 𝑖 𝑠𝑡𝑎𝑟𝑡 indicates the starting time for the crowd to reachthe 𝑖 road node, which is proportional to the distance fromthe node to the root node; 𝑡 𝑖 𝑒𝑛𝑑 indicates the last time for thecrowd to reach the 𝑖 road node; 𝑙 𝑖,𝑡𝑎𝑡𝑎𝑙 is the total distancefrom the starting address to node 𝑖 ; 𝑣 𝑚𝑎𝑥 and 𝑣 𝑚𝑖𝑛 respectivelyrepresent the maximum and minimum speed of the crowd; Δ 𝑡 (cid:48) 𝑖 indicates the difference between the earliest and latest time thatthe flow of people passes the path node. D. Crowd control simulation1) Crowd simulation:
Students depart from the dormitoryand go to the target functional area in turn, and return tothe dormitory after completing the visit. Under quarantineconditions, infected and suspected infected persons need togo to the school hospital for testing and isolation. Each agent is only allowed to move along a given road to the destinationat the permitted time, and the rest of the time is not allowed towalk around. Individuals may be infected inside dormitories,classes, restaurants, roads and so on.
2) Crowd control:
According to the characteristics ofvirus transmission, three control measures have been formu-lated from the perspectives of reducing population densityand improving self-protection, such as batch travel (reduceaggregation by reducing the number of travelers at the sametime), staggered travel (reduce road congestion by controllingtravel time), and isolation prevention (keep suspected patientsaway from the crowd). Based on the experimental results, weanalyze the impact on the results of the virus transmission.IV. E
XPERIMENT
The experiment is based on
𝐶𝑃𝑈 . 𝐺𝐻𝑧 , 𝐺 𝐵 memory,and Windows 10 operating system environment, using 𝐶 + + language and 𝑃𝐸 𝐷𝑆𝐼 𝑀 [31] platform. The system allowsusers to set parameters by themselves to get the infectioncurve, such as the initial total population, the initial numberof patients and the number of days for patients to transitionfrom each state, etc.Taking Zhengzhou University as an example, we scale thenumber of teachers and students in the university proportion-ally. Assuming that there is already an infected patient on thecampus on the first day. According to the infection situationof the groups in different periods, the approximate infectionnumber and infection rates of all teachers and students onthe campus is inferred. In the simulation, each agent is onlyallowed to move along the established road to a specificplace at the specified time, and the rest of the time is notallowed to move around at will. Individuals may be infectedin dormitories, classrooms, restaurants, and roads. The numberof infections at the end of each day is obtained throughthe infection model, and corresponding control measures areimplemented according to the results to reduce the infectionrate. In order to prevent accidental errors in the experiment, thefollowing experimental results are obtained through multipleaverages.
A. Population size
When the total number of people changes, the probability ofindividual contact with each other, movement trends and otherswill change, which will have a certain impact on the spreadand infection of the virus. The population on campus is scaledto different proportions. The initial number of people is set to840, 1260, 1680, and 2520 respectively, and the populationinfection situation within 15 days is calculated through themodel.The results in Figure 6 show that the larger the total numberof people on campus, the more people will eventually beinfected, and the larger the proportion of the total populationwill be. Without constraints, the number of infected people willincrease significantly over time. However, this trend is not ex-actly proportional. When the campus population density is toosmall, the total number of populations should be appropriatelyincreased, and the infection rate will rise relatively slowly;
Fig. 6. Influence of different population sizes on virus transmission.Fig. 7. Infection situations in 21 days before control. when the population density is large, the infection rate willalso increase significantly as the total population increases.Figure 7 shows the proportion of the number of peoplein each state per day when the total number of simulatedpopulations is 1680. The B-lurker curve shows the changeof the number of patients in the incubation period; the B-infected curve shows the change of the number of patients withconfirmed infections; The Berfore control curve represents thechange of the total number of diagnosed and latent personseach day. It can be seen that the curve grows slowly at thebeginning, and then breaks out. Almost everyone is infected onthe 21st day. Based on this, after students return to school, itis necessary to take corresponding protective control measuresto reduce the impact of the virus.
B. Control measures1) Batch travel measures:
From the perspective of timeand space, we formulate intervention measures to reduce therisk of transmission. The first control is to make studentstravel staggered. Since teachers and students have basicallythe same activity areas on campus, there will often be alarge number of people gathering in some areas. Therefore,we should reduce the occurrence of such phenomena andavoid large crowds gathering. Classes are commonly the maincomponent of the daily life of the college group, so firstof all, according to the individual attributes, the class time
Fig. 8. Infection rate curve of 21 days after control of batch travel. is replanned for the student with course tasks. of theteachers and students with course tasks are arranged to haveclasses every morning, and the other half of the students arearranged in the afternoon. In class time, individuals are onlyallowed to stay in the dormitory when they have no class tasks,and all individuals are not allowed to move around the campusat will. Planning student travel in batches in this way cangreatly reduce the degree of crowd density in most cases. Forexample, by reducing the number of people and expanding thephysical space between students during class, it can reduce thecrowdedness of students on the way to the classroom.Comparing the infection results of the population beforeand after the implementation of batch control, as shown inFigure 8. D-lurker represents the change curve of the numberof lurking people per day after the implementation of batchcontrol; D-infected represents the number of people diagnosedevery day after the implementation of batch control; Decreasecontrol represents the total number of infections per day afterthe implementation of batch control. It is found that theupward trend of the curve is relatively flat, and the final totalnumber of infections is reduced by about half compared withthe total number of infections before control. The effect of themeasures after implementation is in line with expectations, andthe spread of the virus can be suppressed to a certain extent.
2) Staggered travel measures:
In the last section, we di-vided the crowd into two groups by replanning the class time,which avoided crowd contact to a certain extent. However, theuniversity group is huge. Under the same batch, students inthe same dormitory building will still experience congestionon the road. In addition to classes, the restaurant is also a high-density crowd gathering place. In meal time, the students willflock to the restaurant. The crowd is very dense on the wayto the restaurant and after arriving in the restaurant.In response to this phenomenon, we put forward restrictionson the prohibition of dinein. The purpose is to reduce thephenomenon of high-density crowds in some areas. Specifi-cally, we will send representatives to take meals back to thedormitory unit and return to the dormitory for meals. Livingwith four students, the plan can reduce about 3/4 of the trafficon the road and the number of people in the restaurant whengoing to eat.In addition, according to the initial location and the destina- tion of each student, we calculate the specific travel time of thestudents in different dormitories. For example, when studentsmove from the dormitory area to other areas of the school, adormitory building determines the travel time according to thelocation between itself and other dormitory buildings and thepath selected by the students to move. By controlling the traveltime in different dormitory buildings, the road utilization at acertain moment can be reduced. Through our algorithm, wecan easily calculate the reasonable departure time of the groupsin each building area, reducing the mutual contact between thegroups.Students are distributed in various dormitory buildings,and teaching areas are also distributed in different areas ofthe campus. On campus under epidemic control, multiplemultitrees are constructed according to the route of all studentsaccording to their starting point. If two or more multitreescontain the same road node and the time overlaps, it meansthat the two paths may collide with pedestrian flows. It needto stagger a little time, adjust the departure time offset Δ 𝑡 ofthe departure point to reduce conflicts. If multiple groups ofpeople pass by the same node on different path trees, but thereis no overlap in the elapsed time, it is not considered to occurcrowds collide.The collision of people traversing each road node, if theroad node 𝑖 appears at the same time in different paths andthe passing time overlaps, we calculate the road congestionwith the following formula; 𝐶 = 𝑛 ∑︁ 𝑖 = 𝑛 ∑︁ 𝑗 = 𝜔 𝑖 𝑗 Δ 𝑡 (cid:48) 𝑖 𝑗 (5)where 𝑛 represents the total number of road nodes in the map; 𝑛 indicates the total number of departure places for the flowof people; 𝜔 𝑖 𝑗 indicates the weight of the flow of people fromthe 𝑗 th starting place passing through the 𝑖 th road node; Δ 𝑡 (cid:48) 𝑖 𝑗 represents the time interval for the flow of people from the 𝑗 thdeparture place to pass through the 𝑖 th road node. Finally, theoffset time of each departure place is adjusted to the minimumvalue, as shown in the following formula: 𝑚𝑖𝑛 (cid:32) 𝑛 ∑︁ 𝑖 Δ 𝑡 𝑖 𝑗 (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) < 𝑗 < 𝑛 (cid:33) (6)In the experiment, the students are evenly distributed in 5dormitory buildings. Preparing for class time, students startfrom the dormitory building to other functional areas of thecampus, and they are required to meet the constraints, that is, max ( 𝑡 𝑖 ) ≤ 𝑚𝑖𝑛 . More ideal results can be obtained throughbrute force traversal and integer planning. The results of thestarting time for classes in different locations are shown inTable IV .After class time, students start from their own building totheir dormitories. According to the distribution of students,the class time is divided into three groups: teaching building,library, others (experimental building, administrative building).The results of the preparation time to get out of class dismissalare shown in Table V.The heat maps in Figure 9 show the crowd density underdifferent conditions on the path. Figure 9(a) is a sample in the TABLE IV T RAVEL TIME FOR CLASS
Building Start TimeDormitory Building 1 0sDormitory Building 2 600sDormitory Building 3 1080sDormitory Building 4 360sDormitory Building 5 120sTABLE V T RAVEL TIME AFTER CLASS
Building Start Timelibrary 0sTeaching building 900sOthers (laboratory building, administrative building) 360s(a) A sample of map (b) Path heat map after staggeredtraveling(c) Path heat map before staggeredtraveling (d) Path heat map after staggeredtravelingFig. 9. Heat map of path density before and after staggered traveling. map. Figure 9(b) means that there are three groups of peoplefrom different locations moving in the same direction at thesame time. Figure 9(c) represents the density of people on eachpath that is not controlled. It can be seen that when pedestrianson multiple paths move toward the same destination at thesame time, there will be a high density of people. Figure 9(d)shows that by adjusting the travel time, the figure enablesstudents to implement non-intersection travel measures, whichcan effectively reduce the crowd density on the road.As shown in Figure 10, T-control represents the changecurve of the total number of persons in the incubation periodand infected persons every day after the implementation ofstaggered travel control measures. It can be seen that theincreasing trend is slow compared with the other two redcurves. By implementing control measures to reduce popu-lation density, the probability of virus transmission can befurther reduced.
3) Isolation control measures:
Because of the transmissi-bility of the virus, once a confirmed patient is found, he or sheshould be isolated immediately [32]. Taking the compulsorymeasures can prevent the spread of the virus from the root. If
Fig. 10. 21-day infection rate curve after staggered travel.Fig. 11. The infection rate curves under different states in the disease. a confirmed patient is found on the campus, the student willbe immediately sent to the school hospital for closed isolation.By tracing the track of the student, those who have been inclose contact with him are regarded as suspected cases andsent to the school hospital for isolation and observation [33].However, since some virus carriers may still have noobvious symptoms of infection after the incubation period,that is, asymptomatic patients, such patients need to rely onmedical methods to determine their physical health, whichmeans the difficulty of epidemic investigation and control isfurther increased. Three sets of experiments show the changesin infection when there are asymptomatic patients.The results are shown in Figure 11, the blue curve indicatesthe changing trend of the infection rate of a person infectedwith the virus on the first day and being isolated and treatedafter 7 days of infection; The green curve shows the trendof the daily infection rate of the population when one personis infected on the first day and can be isolated in time; Thered curve represents the daily infection trend when one personinfected with the virus on the first day and all patients willhave a probability of 0.1 as asymptomatic infections. Theappearance of asymptomatic patients will make the conditioncomplicate. Only by detecting all virus carriers can it be pos-sible to completely control the spread of the virus, otherwisethe virus will still spread on a large scale.As shown in Figure 12, the three curves of I-lurker, I-infected, and Isolate control respectively represent the chang-
Fig. 12. The infection rate curve after the implementation of quarantinemeasures.Fig. 13. The comparison under different measures without control, batching,staggered travel, and isolation. ing trends of the number of suspected cases, the number ofconfirmed persons, and the total number of infections after theimplementation of mandatory isolation measures. The numberof people infected each day after the quarantine measures isless than the number of patients before the implementationof the quarantine measures, and the total number of peopleinfected on the 21st day is only . Compared with thecontrol measures in the previous two sections, it is provedthat the implementation of isolation measures can effectivelyreduce the probability of students infected with the virus.As shown in Figure 13, experimental results show that in ahigh-density and closed area similar to colleges and universi-ties, if one person is infected with the virus, there will be ahigh probability of infection to others, even if control measuresare implemented. After implementing compulsory isolationmeasures, timely isolation and treatment of suspicious patientswill further slow down the spread of the virus, but over time,it is still difficult to achieve zero spread of the virus.
C. Proportion of self-protection population
Since the strong transmission of the novel coronavirus, somepeople have high awareness of protection. Due to individualdifferences, the infection probability of each person is notexactly the same. In addition to the protection measuresimplemented by universities on teachers and students, individ-
Fig. 14. The infection curve of self-protection rate. uals also need strengthen self-protection. For example, takesome self-protection measures such as wearing a mask andconsciously keeping a distance from others. After the groupadopts protective measures, the spread of the virus will bereduced, and the group infection rate will also decrease. Butthe probability will change according to the change of thegroup protection ratio, so we explore the impact of differentpopulation protection in universities on the trend of virusinfection.Figure 14 shows the impact of the self-protection rate ofdifferent groups in universities on the virus infection rate inthe group within 21 days. The green, red, blue, and yellowcurves represent the daily viral infection rate of the populationwhen the population protection rate is , , , and . On the 21st day, when of the people in collegesand universities take self-protection measures, the green curveshows that the virus infection rate is . The result is muchhigher than the result under the same conditions that thenumber of people taking protective measures reaches andabove. The more people who take protective measures, thelower the infection rate. From the overall experimental results,it can be inferred that if everyone takes protective measures,the infection rate will be lower than the infection rate in thecase of a self-protection rate of . Therefore, universitiesshould actively call on all teachers and students to protectthemselves in order to better control the spread of the virus.V. C ONCLUSION
In response to the novel coronavirus pneumonia broke outat the end of 2019, the states has implemented a series ofmeasures to prevent a large number of people from gatheringand aggravate the epidemic. Take the problem of virus trans-mission after returning to school as an example, we proposesa campus virus infection and control simulation (CVICS)model that is oriented to a closed environment, frequentpopulation contact, and strong mobility. Constructing an agent-based simulation, taking into account the differences betweenindividuals, we introduce the average field theory to micro-simulate the infection situation of each individual every day.The experimental results show that the model can calculate thedaily population infection trend and individual infection status,and through batch travel, staggered travel, isolation and other control measures, it can effectively reduce the probability ofpopulation infection and curb the rapid spread of the virus to acertain extent. During the epidemic, a series of tough measuresshould be taken to reduce crowd gathering. Once suspectedpatients are found, compulsory measures should be taken toisolate them under medical observation. When the isolationis strong, the source of infection is blocked, and the spreadof novel coronavirus will be better controlled. As individuals,we should try our best to avoid crowd gathering, reduce crowdcontact, and enhance self-protection.In the future, in addition to considering existing controlmeasures, resource allocation needs to be considered, such asadding disinfection and vaccine measures, to further improvethe virus infection model accuracy. The improved model willsimulate the more complex crowd flow in large-scale areas,fitting real infection data as much as possible.R EFERENCES[1] W. H. Organization et al. , “Global research on coronavirus disease(covid-19),”
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Journal oftheoretical biology , vol. 229, no. 1, pp. 119–126, 2004. Pei Lv received the Ph.D. degree from the StateKey Laboratory of CAD&CG, Zhejiang UniversityHangzhou, China, in 2013. He is an AssociateProfessor with the School of Information Engi-neering, Zhengzhou University, Zhengzhou, China.His research interests include computer vision andcomputer graphics. He has authored more than 30journal and conference papers in the above areas,including the IEEE T RANSACTIONS ON I MAGEP ROCESSING , the IEEE T RANSACTIONS ONC IRCUITS AND SYSTEMS FOR VIDEO TECH-NOLOGY, CVPR, ACM MM, and IJCAI.
Quan Zhang received the B.S. degree from theComputer Science and Technology Department,Putian University, China, in 2018. He is currentlya master student in the School of Information Engi-neering of the Zhengzhou University. His researchinterests include computer graph, crowd simulation.
Boya Xu received the B.S. degree from the Soft-ware Engineering Department, Zhengzhou Univer-sity, China, in 2018. She is currently a master studentin the School of Information Engineering of theZhengzhou University. Her research interests includecomputer graph, crowd simulation.
Ran Feng received her B.Sc degree in ComputerScience and Technology from Zhengzhou Univer-sity. Zhengzhou, China, in 2012 and M.Sc degreein Computer Science from HongKong University.HongKong, China, in 2015.She is currently a Ph.D.student in the School of Information Engineeringof Zhengzhou Uninversity. Her research interestsinclude evolutionary computation and multiobjectiveoptimization.
Chaochao Li received his Ph.D. degree from theSchool of Information Engineering, Zhengzhou Uni-versity, Zhengzhou, China. His current researchinterests include computer graphics and computervision. He is currently an assistant research fel-low with the School of Information Engineering,Zhengzhou University, Zhengzhou, China. He hasauthored over 6 journal and conference papers in-cluding the IEEE TRANSACTIONS ON AFFEC-TIVE COMPUTING, IEEE TRANSACTIONS ONINTELLIGENT TRANSPORTATION SYSTEMS,and IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS:SYSTEMS.
Junxiao Xue is an associate professor in the Schoolof Software of Zhengzhou University, China. His re-search interests include virtual reality and computergraphics. He received his Ph.D in 2009 from theSchool of Mathematical Sciences, Dalian Universityof Technology, China.
Bing Zhou received the B.S. and M.S. degrees incomputer science from Xian Jiao Tong University,Xian, China, in 1986 and 1989, respectively, andthe Ph.D. degree in computer science from BeihangUniversity, Beijing, China, in 2003. He is currentlya Professor with the School of Information Engi-neering, Zhengzhou University, Zhengzhou, China.His research interests include video processing andunderstanding, surveillance, computer vision, andmultimedia applications.