# On the Sustainability of Shared Mobility Since COVID-19: From Socially Structured to Social Bubble Vanpooling

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## Abstract

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## 1. Introduction

## 2. Public Transport, Shared Mobility, and the Spread of COVID-19

- (1)
- as a vector that facilitates the spread of communicable diseases from one place to another (mobility as a vector) [27]. Communicable diseases spread over space when infectious persons move (using transportation modes) from one location to another, where they might infect other persons.
- (2)
- as an environment (transportation means and settings) where people are confined, crowded, and might become infected (mobility as an activity) [28].

## 3. From Socially Structured Vanpooling to Social Bubble Vanpooling

#### 3.1. Social Bubbles of Riders

#### 3.2. Spatio-Temporal Pooling Phase

- For each pair of clusters ${C}_{i}$ and ${C}_{j}$, compute$$\begin{array}{c}d({C}_{i},{C}_{j}){\omega}_{s}=\left[{\left(\sum _{i=1}^{|{C}_{i}|}\frac{Lo{n}_{i}}{|{C}_{i}|}-\sum _{j=1}^{|{C}_{j}|}\frac{Lo{n}_{j}}{|{C}_{j}|}\right)}^{2}+\right.{\left.{\left(\sum _{i=1}^{|{C}_{i}|}\frac{La{t}_{i}}{|{C}_{i}|}-\sum _{j=1}^{|{C}_{j}|}\frac{La{t}_{j}}{|{C}_{j}|}\right)}^{2}\right]}^{\frac{1}{2}}\hfill \\ \hfill +{\omega}_{t}max({\tau}_{max}^{i}-{\tau}_{min}^{j},{\tau}_{max}^{j}-{\tau}_{min}^{i})\end{array}$$
- Two clusters ${C}_{i}$ and ${C}_{j}$ are merged if:$$d({C}_{i},{C}_{j})\le {d}_{max},$$

#### 3.3. Social Bubble Pooling Phase

- Commuter i is a relative of commuter j (${\lambda}_{i\to j}+=s$).
- Commuter i works with commuter j (${\lambda}_{i\to j}+=w$).
- Commuter i follows commuter j on social networks (${\lambda}_{i\to j}+=l$).
- Commuter i has blocked j on social networks (${\lambda}_{i\to j}-=l$).
- Commuter i has expressly declined a ride share with j (${\lambda}_{i\to j}-=l$).

**Remark 1.**

#### 3.4. Operating Cost of Pandemic-Resilient Pooling

**Remark 2.**

**The cost of not being flexible:**

**Infection incidence:**the probability ${p}_{i}$ can be calculated using a disease spread model whenever contact tracing is implemented. Otherwise, we estimate an overall probability of infection incidence p, such that $\forall i,{p}_{i}=p$. p is merely calculated based on the number of susceptible people in the population of interest.

## 4. Simulation-Based Experiments

#### 4.1. Epidemiological Model

- During any day of the simulation, commuters can be either susceptible, exposed, recovered, asymptomatic infectious, pre-symptomatic infectious, or symptomatic infectious (to reflect the case of travelers who develop mild symptoms and not tested but still commute and do not comply to self-isolation instructions).
- Commuters who are asymptomatic infectious, pre-symptomatic infectious, and symptomatic infectious spread the disease over susceptible commuters with different transmission levels.
- Isolated or quarantined commuters temporarily cannot travel until they are recovered (or test negative after the quarantine period in which case they become susceptible), which means that pools with isolated or quarantined commuters may need to be updated to find new commuters (according to the flexible re-pooling scheme presented in Section 3.4).
- Recovered commuters need to resume their travel activity and need to either join their initial pools or join a new pool.
- Deceased commuters are permanently removed and their initial pools may need to be updated.
- The same model applies for drivers who can be infectious/become infected. In the simulation we assume that isolated or quarantined drivers will be replaced by new ones, which means that buses are still available for commuting.
- In case the driver or a member of a pool tests positive, the driver and all the pool members are quarantined and the bus may be used for a different pool of commuters.

#### 4.2. Agent-Based Model and Activity Patterns

- Initialize the population of commuters and vans;
- Identify the list of pools and assign commuters to vans according to the SBV algorithm defined in Section 3.4;
- Determine the initial number and location of initially infected commuters
- For every simulation day t:
- (a)
- If working day, then:
- -
- Make the ${k}^{th}$ trip of every van j from home to the main activity location (work, school, university, etc.);
- -
- Calculate the probability of infection ${p}_{i}^{{V}_{j}^{k}}\left(t\right)$ of every individual i in every van j making the ${k}^{th}$ trip from home to the main activity location;
- -
- Calculate the probability of infection of every individual in the main activity context;
- -
- Make the $k+{1}^{th}$ trip of every van j from the main activity location to home;
- -
- Calculate the probability of infection ${p}_{i}^{{V}_{j}^{k+1}}\left(t\right)$ of every individual i making the $k+{1}^{th}$ trip of every van j from home to the main activity location;

- (b)
- Calculate the probability of infection of every individual at home;
- (c)
- Apply the epidemiological model and change the states of commuters/drivers;
- (d)
- Apply the intervention model (quarantine after contact tracing and/or testing), if any;
- (e)
- Reconstruct or update pools and reassign commuters to vans (flexible reassignment), if needed;

- Update the infection incidence probability p using $p=\frac{I}{T}$, where I is the number of reported infected cases and T is the size of the total population;
- Stop simulation at the end-of simulation period or if there are no more infected individuals.

#### 4.3. Experimental Setup

Parameter | Meaning | Value | Reference |
---|---|---|---|

${p}_{i}^{{V}_{j}^{k}}\left(t\right)$ | Probability that a susceptible individual i traveling in the ${k}^{th}$ trip of the van ${V}_{j}$ on day t be infected | Calculated in the simulation | [76] |

${E}_{p}$ | Exposure (latent) period (in days) | 2.5 | [81] |

$I{P}_{p}$ | Pre-symptomatic infectious period (in days) | 1 | [81] |

${I}_{p}$ | Infectious period (in days) | 6 | [81] |

$I{S}_{p}$ | Isolation period (in days) | 15 | National policy of Oman |

${Q}_{p}$ | Quarantine period (in days) | 14 | National policy of Oman |

$\beta $ | Infection rate of COVID-19 | 2.5 | Ministry of Health, Oman |

${D}_{r}$ | Death rate | 0.0107 | Ministry of Health, Oman |

${R}_{r}$ | Recovery rate | 0.9252 | Ministry of Health, Oman |

- Trip-based vanpooling, where pools of riders are formed for every trip.
- Long-term committed vanpooling (pools are formed of the same riders during the period of service) without social bubbles, i.e., pools are formed using only the spatio-temporal clustering step.
- Social bubble based vanpooling proposed in this paper.

## 5. Results and Discussion

#### 5.1. Scenario 1

#### 5.2. Scenario 2

- Enforcing contact tracing and quarantine is more effective in controlling the spread of the disease when the bubble-based ridesharing scheme is adopted as a commuting mode.
- It is possible to sustain the transportation service without compromising the efforts to mitigate the spread of the pandemic.

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**An example of weighted label propagation in a small network of four commuters. From the initial weights of the directed edges in (

**a**), the different $\lambda ij,\phantom{\rule{3.33333pt}{0ex}}1\le i,j\le 4,i\ne j$ are calculated (

**b**) and used to propagate the initial labels and create two socially cohesive groups in (

**c**).

**Figure 2.**Example of ridesharing service disruption caused by the infection and isolation of some riders (highlighted in red) with 3 vans and 18 riders (

**a**). The operating scheme uses a rigid bubble decomposition (

**b**) and using flexible reassignment (

**c**).

**Figure 5.**Epidemiological spread in scenario 1 using trip-based ridesharing (${R}_{0}=1.82$) (

**a**), long-term committed ridesharing (${R}_{0}=1.69$) (

**b**), and social bubble vanpooling (SBV) (bubble-based ridesharing (${R}_{0}=1.65$)) (

**c**).

**Figure 6.**Epidemiological spread in scenario 2 using trip-based ridesharing (${R}_{0}=1.44$) (

**a**), long-term committed ridesharing (${R}_{0}=1.23$) (

**b**), and social bubble vanpooling (bubble-based ridesharing (${R}_{0}=1.09$)) (

**c**).

**Table 1.**Comparison between the constraints in socially structured vanpooling (SSV) [23] and social bubble vanpooling (SBV).

Symbol | Meaning | SSV | SBV |
---|---|---|---|

$R{O}_{i}$ | Rider i’s origin (home) geographic location (longitude, latitude) | ✓ | ✓ |

$R{D}_{i}$ | Rider i’s activity destination geographic location (longitude, latitude) | ✓ | ✓ |

${P}_{i}$ = [${D}_{start}$, ${D}_{end}$] | Start and end dates of the service period of the rider i | ✓ | ✓ |

${\tau}_{min}^{i}$ | Rider i’s earliest time interval to start the trip | ✓ | ✓ |

${\tau}_{max}^{i}$ | Rider i’s latest time interval to start the trip | ✓ | ✓ |

${T}_{Forth}^{i}=[{\tau}_{min}^{i},{\tau}_{max}^{i}]$ | Travel time window of rider i from home to the activity’s destination location | ✓ | ✓ |

${T}_{Back}^{i}=[{\tau}_{min}^{i},{\tau}_{max}^{i}]$ | Travel time window of rider i from the activity location to home | ✓ | ✓ |

$Pref{T}^{i}$ = ({day}, ${T}_{Forth}^{i}$, ${T}_{Back}^{i}$) | Rider i’s slots, where every slot is defined by a set of days and travel time windows | ✓ | ✓ |

${R}_{price}^{i}=[min,max]$ | Rider i’s budget range | ✓ | ✓ |

${R}_{age}^{i}$ | Rider i’s age | ✓ | ✓ |

${R}_{hrisk}^{i}$ | Rider i’s health risk level with respect to communicable diseases, value $\in \left[\right[1,5\left]\right]$, 1 = very low risk level, 2 = low risk level, 3 = medium risk level, 4 = high risk level, and 5 = very high risk level | ✗ | ✓ |

${R}_{socialG}^{i}$ | Rider i’s social preferences: ${C}_{socialG}^{i}\left(j\right)={w}_{ij}$, where j is the ${j}^{th}$ rider in the same spatial cluster as i, ${w}_{ij}\in \left[[-5,5]\right]$ | ✓ | ✗ |

${R}_{safety}^{i}$ | Rider i’s safety value $\in \left[\right[1,5\left]\right]$, 1 = not important, 5 = extremely important | ✓ | ✗ |

${R}_{comf}^{i}$ | Rider i’s comfort value $\in \left[\right[1,5\left]\right]$, 1 = not important, 5 = extremely important | ✓ | ✗ |

${R}_{exp}^{i}$ | Rider i’s value for driver experience $\in \left[\right[1,5\left]\right]$, 1 = not important, 5 = extremely important | ✓ | ✗ |

${R}_{clean}^{i}$ | Rider i’s value for van cleanness $\in \left[\right[1,5\left]\right]$, 1 = not important, 5 = extremely important | ✓ | ✗ |

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## Share and Cite

**MDPI and ACS Style**

Haddad, H.; Bouyahia, Z.; Horchani, L.
On the Sustainability of Shared Mobility Since COVID-19: From Socially Structured to Social Bubble Vanpooling. *Sustainability* **2022**, *14*, 15764.
https://doi.org/10.3390/su142315764

**AMA Style**

Haddad H, Bouyahia Z, Horchani L.
On the Sustainability of Shared Mobility Since COVID-19: From Socially Structured to Social Bubble Vanpooling. *Sustainability*. 2022; 14(23):15764.
https://doi.org/10.3390/su142315764

**Chicago/Turabian Style**

Haddad, Hedi, Zied Bouyahia, and Leila Horchani.
2022. "On the Sustainability of Shared Mobility Since COVID-19: From Socially Structured to Social Bubble Vanpooling" *Sustainability* 14, no. 23: 15764.
https://doi.org/10.3390/su142315764