SIRS Model of Passengers’ Panic Propagation under Self-Organization Circumstance in the Subway Emergency

Zhao, Haifeng; Jiang, Jie; Xu, Rui‐hua; Yang, Ye

doi:10.1155/2014/608315

Cited by 16 publications

(18 citation statements)

References 48 publications

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“…Based on system dynamics and transmission dynamics, this paper establishes an improved dynamic differential equation of the SIRS infectious disease model by using formulas (1)- (3), which are used to describe and model the evolution of passengers' panic in subway cars with guidance information when a sudden crisis takes place. Its parameters and state transformation relations are shown in Figure 1.…”

Section: Dynamic Sirs Model and Parametersmentioning

confidence: 99%

“…ere are N � 1400 passengers in the subway car. We set the model parameters as the length and width of the subway car, which is consistent with reference [3]. Considering the offpeak hours, the number of people in the subway cars has not reached the peak, and they are not crowded.…”

Section: Dynamic Simulation Of Panic Diffusion With Guidancementioning

confidence: 99%

“…Since the 1970s, subway stations around the world have seen frequent security incidents, such as terrorist bombings, riots, crowds, and stampedes [2]. However, due to the high population density of the subway and the small enclosed space, panic caused by emergencies can spread rapidly [3]. In serious cases, traffic accidents occur in chaos, which will further aggravate the impact of the whole event.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Spreading Model of Passenger Group Panic considering Official Guidance Information in Subway Emergencies

Tang

Wang

2019

Mathematical Problems in Engineering

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Safety concerns are increasing as rail transportation develops at a fast pace. When emergencies erupt in the course of transportation, panic will spread among passengers. Subway operators should understand how the emotions of passengers spread and how the guidance instructions work, in order to effectively deter the transmission of panic. Based on the models of system dynamics, transmission dynamics, and contagious disease, the essay constructs a dynamic transmission model for passenger panic inside the carriage, incorporating the official guidance instructions. Then, the essay utilizes Routh–Hurwitz criteria and analyzes the stability equilibrium of the dynamic differential equation. Mathematical analysis and simulation tests have verified the validity of the model and stability conditions. Finally, it is proved in the essay by mathematical analysis and simulation tests that official guidance instructions can effectively control the spread of panic and quickly stabilize the system. Thus, the essay helps subway operators to come up with clear official guidance, so as to find quick solutions and prevent escalation of panic due to lack of trust.

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Section: Dynamic Sirs Model and Parametersmentioning

confidence: 99%

Section: Dynamic Simulation Of Panic Diffusion With Guidancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamic Spreading Model of Passenger Group Panic considering Official Guidance Information in Subway Emergencies

Tang

Wang

2019

Mathematical Problems in Engineering

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“…Generally, these epidemic models are utilized when there is an hypothesis that the removed population could move to the susceptible class after being healed from a disease due to the loss of their immunity. Other studies which were based on SIRS models can be found in [3,4,5]. Also, since our modeling framework here, is in the form of a discrete-time SIRS epidemic system, we cite works of Masaki Sekiguchi in [6] and with Emiko Ishiwata in [7].…”

Section: Introductionmentioning

confidence: 99%

Travel-blocking Optimal Control Policy on Borders of a Chain of Regions Subject to SIRS Discrete Epidemic Model

Bidah

Rachik

Zakary

et al. 2018

AJRID

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With thousands of people moving from one area to another day by day, in a chain of regions tightly more interconnected than other regions in a given large domain, an epidemic may spread rapidly around it from any point of borders. It might be sometimes urgent to impose travel restrictions to inhibit the spread of infection. As we aim to protect susceptible people of this chain to contact infected travelers coming from its neighbors, we follow the so-called travel-blocking vicinity optimal control approach with the introduction of the notion of patch for representing our targeted group of regions when the epidemic modeling framework is in the form of a Susceptible-Infected-Removed-Susceptible (SIRS) discrete-time system to study the case of the removed class return to susceptibility because of their short-lived immunity. A discrete version of the Pontryagin’s maximum principle is employed for the characterization of the travel-blocking optimal control. Finally, with the help of discrete progressive-regressive iterative schemes, we provide cellular simulations of an example of a domain composed with 100 regions and where the targeted chain includes 7 regions.

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“…In epidemics, we can sometimes face situations where a removed population has lost its immunity after being healed from an infection, and then, it moves to the susceptible compartment as studied in [4], [5] and [6]. Compartmental models in the form of S-Exposed-I-R-S (SEIRS) models, could well-describe these phenomena.…”

Section: Introductionmentioning

confidence: 99%

A Multi-Regions SIRS Discrete Epidemic Model With a Travel-Blocking Vicinity Optimal Control Approach on Cells

Abouelkheir

Kihal

Rachik

et al. 2017

BJMCS

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Compared to Susceptible-Infected-Removed Susceptible (SIRS) systems, where it is supposed that a removed population has lost its immunity after being healed from an infection and moves to the susceptible compartment, the S-Exposed-I-R-S (SEIRS) compartmental models, consider also, the presence of an additional compartment named by the variable E which could represent the number of asymptomatic infected individuals, people who are not yet infectious or just exposed to infection. Based on these assumptions, we devise a multi-regions SEIRS discrete-time model which describes infection dynamics due to the presence of an epidemic in regions that are connected with their neighbors by any kind of anthropological movement. The main goal from this kind of modeling, is to introduce after, controls variables which restrict movements of the infected individuals coming from the vicinity of the region targeted by our control strategy we call here by the travel-blocking vicinity optimal control approach. A grid of colored cells is presented to illustrate the whole domain affected by the epidemic while each cell represents a sub-domain or region. In order to illustrate an example of these SEIRS dynamics, we choose an example of infection which is supposed starting from only one cell located in one of the corners of the grid, while the region aiming to control, is supposed to be located in the 2nd line and 4th column of the grid. It is important to note, this optimization approach could be applied to any cell of the grid, and the source of infection could also be supposed to start from any cell. In fact, the example is presented, just to show the effectiveness of the proposed control strategy when it is applied to a cell with an important number of connections (i.e. with 8 neighboring cells in our simulations).

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SIRS Model of Passengers’ Panic Propagation under Self-Organization Circumstance in the Subway Emergency

Cited by 16 publications

References 48 publications

Dynamic Spreading Model of Passenger Group Panic considering Official Guidance Information in Subway Emergencies

Dynamic Spreading Model of Passenger Group Panic considering Official Guidance Information in Subway Emergencies

Travel-blocking Optimal Control Policy on Borders of a Chain of Regions Subject to SIRS Discrete Epidemic Model

A Multi-Regions SIRS Discrete Epidemic Model With a Travel-Blocking Vicinity Optimal Control Approach on Cells

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