# A Complete Information Interaction-Based Bus Passenger Flow Control Model for Epidemic Spread Prevention

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## Abstract

**:**

## 1. Introduction

## 2. Problem Description

## 3. A Bus Passenger Flow Interactive Control Model Based on the Impact of COVID-19 Spread

#### 3.1. Basic Assumptions

- The travel needs of passengers are known, that is, the pick-up and drop-off locations, regardless of the passenger travel time window and transfer;
- The bus obtains the travel needs of passengers in advance, leaves the station on time according to the departure schedule, and runs according to the fixed bus line. The bus will not accept any changes in passenger destination after departure;
- The determination of the spread of the epidemic is based on the risk of transmission on the bus, not the risk of waiting at a stop and getting on and off the bus;
- Each passenger pays the same fare for one trip, regardless of the distance traveled. In addition, during the bus ride, there are no traffic jams or emergencies on the road, and the bus moves forward at a constant speed.

#### 3.2. Basic Model of Infection Transmission via Bus Transport

#### 3.3. Complete Information Interaction-Based Bus Passenger Flow Control Model

## 4. Solving the Model

## 5. Case Analysis

#### 5.1. Research Object

#### 5.2. Value Calibration

^{3}. The novel coronavirus pneumonia virus is highly contagious, but considering the limited full load rate of buses and that the range in the bus was small, the value of the contact infection rate $\mathsf{\alpha}$ was set at 0.4.

#### 5.3. Analysis of the Results

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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Bus Stop | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 0 | 2 | 2 | 2 | 0 | 2 | 0 | 3 | 0 | 2 | 0 | 0 | 0 | 0 | 0 |

2 | 0 | 0 | 0 | 2 | 0 | 0 | 2 | 1 | 0 | 1 | 0 | 2 | 2 | 0 | 1 |

3 | 0 | 0 | 0 | 1 | 3 | 3 | 0 | 2 | 2 | 0 | 3 | 0 | 0 | 0 | 0 |

4 | 0 | 0 | 0 | 0 | 2 | 0 | 2 | 0 | 2 | 0 | 1 | 2 | 0 | 0 | 1 |

5 | 0 | 0 | 0 | 0 | 0 | 1 | 4 | 2 | 2 | 1 | 2 | 0 | 0 | 0 | 0 |

6 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 2 | 3 | 0 | 0 | 0 | 2 | 0 |

7 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 0 | 1 | 3 | 1 |

8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 0 | 4 | 2 | 1 | 0 |

9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 2 | 2 | 0 | 1 | 3 |

10 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 3 | 2 | 0 |

11 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 3 | 2 |

12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 0 |

13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 3 |

14 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3 |

15 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Bus Stop | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

on | 13 | 11 | 14 | 10 | 12 | 9 | 9 | 9 | 11 | 7 | 7 | 2 | 6 | 3 | 0 |

off | 0 | 2 | 2 | 5 | 5 | 6 | 9 | 9 | 10 | 12 | 10 | 12 | 12 | 15 | 14 |

Control Scheme | Occupancy Rate | Infection Probability | Epidemic Safety Cost | Passenger Travel Cost | Bus Operation Cost | Weighted Total Cost | |
---|---|---|---|---|---|---|---|

/ | / | 100.00% | 0.104011 | 210.62 | 415.17 | −146 | 180.21 |

y_{1} = 0 | / | 89.43% | 0.089809 | 181.86 | 437.11 | −120 | 172.54 |

y_{12} = 0 | 87.80% | 0.089409 | 181.05 | 440.48 | −116 | 173.53 | |

y_{2} = 0 | / | 91.06% | 0.085408 | 172.95 | 433.73 | −124 | 165.72 |

y_{12} = 0 | 89.43% | 0.085009 | 172.14 | 437.11 | −120 | 166.71 | |

y_{14} = 0 | 88.62% | 0.084809 | 171.74 | 438.79 | −118 | 167.20 | |

y_{3} = 0 | / | 88.62% | 0.089409 | 181.05 | 438.79 | −118 | 172.79 |

y_{4} = 0 | / | 91.87% | 0.091610 | 185.51 | 432.04 | −126 | 172.51 |

y_{12} = 0 | 90.24% | 0.091209 | 184.70 | 435.42 | −122 | 173.50 | |

y_{14} = 0 | 89.43% | 0.091009 | 184.29 | 437.11 | −120 | 174.00 | |

y_{12} = y_{14} = 0 | 87.80% | 0.090609 | 183.48 | 440.48 | −116 | 174.99 | |

y_{5} = 0 | / | 90.24% | 0.093810 | 189.97 | 435.42 | −122 | 176.66 |

y_{12} = 0 | 88.62% | 0.093410 | 189.16 | 438.79 | −118 | 177.65 | |

y_{14} = 0 | 87.80% | 0.093210 | 188.75 | 440.48 | −116 | 178.15 | |

y_{6} = 0 | / | 92.68% | 0.094610 | 191.59 | 430.36 | −128 | 175.42 |

y_{12} = 0 | 91.06% | 0.094210 | 190.78 | 433.73 | −124 | 176.41 | |

y_{13} = 0 | 87.80% | 0.092810 | 187.94 | 440.48 | −116 | 177.66 | |

y_{14} = 0 | 90.24% | 0.094010 | 190.37 | 435.42 | −122 | 176.91 | |

y_{12} = y_{14} = 0 | 87.80% | 0.093610 | 189.56 | 440.48 | −116 | 178.63 |

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## Share and Cite

**MDPI and ACS Style**

Hu, X.; Xu, Y.; Guo, J.; Zhang, T.; Bi, Y.; Liu, W.; Zhou, X.
A Complete Information Interaction-Based Bus Passenger Flow Control Model for Epidemic Spread Prevention. *Sustainability* **2022**, *14*, 8032.
https://doi.org/10.3390/su14138032

**AMA Style**

Hu X, Xu Y, Guo J, Zhang T, Bi Y, Liu W, Zhou X.
A Complete Information Interaction-Based Bus Passenger Flow Control Model for Epidemic Spread Prevention. *Sustainability*. 2022; 14(13):8032.
https://doi.org/10.3390/su14138032

**Chicago/Turabian Style**

Hu, Xinghua, Yimei Xu, Jianpu Guo, Tingting Zhang, Yuhang Bi, Wei Liu, and Xiaochuan Zhou.
2022. "A Complete Information Interaction-Based Bus Passenger Flow Control Model for Epidemic Spread Prevention" *Sustainability* 14, no. 13: 8032.
https://doi.org/10.3390/su14138032