Crowd infection and its prevention strategy in a subway station based on social force model

. With the development of society, crowds in public buildings are dense, and the subsequent spread of diseases in places with high population density has attracted widespread attention. In the real situation, the spread of the disease has its complexity, such as the influence of factors such as the movement of people and the intervention of external measures, so it is necessary to further refine the description of the process of infection transmission. Based on the social force model, this article focuses on the impact of microscopic crowd movement in public places on the dynamics of infection. Taking a typical pedestrian exit process in a subway station as an example, we numerically simulated the infection problem among small-scale people in public places, observed the impact of pedestrian movement characteristics on infection transmission, put forward corresponding prevention and control measures, and verified the effectiveness of the measures.


Introduction
There is a strong link between the movement of people and the spread of diseases, from the global spread of infectious diseases to the cross-infection in a subway station. By tracing the movement of infected people, the scope of the disease can be roughly predicted, and effective prevention and control measures can be taken.
Li et al. Combined SEIR model and urban traffic network model, proposed a simulation system suitable for urban epidemic transmission in China [1] . Based on the warehouse model, Chen Renxia [2] and Zhao Jing [3] introduced indirect infection rate and non-uniform transmission respectively. Yu Hong [4] studied the effects of different susceptibility, infectivity, individual movement and infection cycle based on the complex network theory. Based on the social force model, Namilae [5] simulated the impact of contact between passengers during boarding and disembarkation on the transmission of infection, and evaluated the impact of  The social force model [6] is based on Newton's second law of motion, takes each pedestrian as the research object, analyzes its force, and studies the movement of the crowd. The relationship between the force and acceleration of pedestrian i is shown in formula (1) : The resultant force received by pedestrians includes three parts. The first part 0 f i is the driving force of pedestrians. The second part f ij refers to the force of other pedestrians acting on pedestrian. The third part f iw is the force of obstacles such as walls on pedestrians.Specific calculation references [6] . Therefore, this paper determines the direction of pedestrian expected speed by calculating the flow field velocity vector by lattice Boltzmann method. D2Q9 model is adopted, and the boundary condition is set as rebound boundary. In order to prevent the emergence of vortex, a small Reynolds number is used to determine the initial state parameters.
The judgment method of pedestrian infection is as follows: in the process of crowd movement, when the distance between the susceptible person and the infected person is less than or equal to the infection radius Inf r and remains within this range for a certain time, it is considered to have come into contact with the infected person. Next, the system will generate represents susceptible, 1 represents latent, and 2 represents infected. The existence of the remover (rehabilitator) is not considered in this paper . Here, 2.5 seconds is taken according to the literature [5] . Delyt is the total time after infection ( Statistically, it is the ratio of the number of infected persons to the number of exposed persons.

Fig. 1. Simulation scene
Referring to the CAD drawings of existing typical subway stations, the simulation scene set in this paper is shown in Figure 1, -1F is the platform layer and 1F is the station hall layer. The expected speed of pedestrians meets the uniform distribution [7] , and the individual size is taken according to relevant standards [8] .

Results
As shown in Figure 2  the contact times results is larger. This may be because pedestrians have the following effect [9] . Due to the following effect, most of the infected people are pedestrians around the initial infected people. Therefore, the location of the initial infected people will have an important impact on the number of infected people. We simulated the infection situation under different infection radius and basic infection number, and the results are shown in Figure 3 (b-c). It can be seen that in any case, the number of infected people increases with the increase of the total number of outbound people.

Analysis of pedestrian aggregation in subway station
As shown in Figure 4

Increase pedestrian spacing and expected speed
The parameter Bi in the social force model represents the characteristic length of individual social repulsion force to other pedestrians. The larger the value is, the greater the repulsion force between pedestrians is. The larger the corresponding distance between pedestrians is. Therefore, to increase the distance between pedestrians, only increase the value of i B , and the results are shown in Figure 5. Figure 5 (a) shows that the number of infected people decreases when the pedestrian spacing increases; The simulation results in Figure 5

Guide pedestrians to take stairs
It can be seen from Figure 7 (a) that when walking from stairs, the space range is larger, and the distance between crowds increases correspondingly, and the contact between crowds decreases. The comparison chart of infection probability density in Fig.7(b-c) also illustrates this situation. The infection situation at the elevator entrance has decreased. Therefore, pedestrians should be guided to use stairs to reduce the possibility of infection during an epidemic.