# Digital Twin of COVID-19 Mass Vaccination Centers

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Problem Description

## 4. Materials and Methods

#### 4.1. Simulation Model

^{group}which is the size of the group that enters the system at a specific instant and has a probability P

^{group}related to each size. Another parameter is the time between two consecutive group arrivals (t

^{arrival}) which determines the hourly arrival rate. The second module is the queue of entry control which represents the waiting before the entry control phase. This module is characterized by Q

_{A}, the maximum number of places to dedicate to the queue in phase A. This phase is the only one that includes a single queue for each resource, while the others have just one queue for the entire phase to increase the efficiency of the system. When at least one resource in phase A is idle, the patient proceeds to the performance of entry control module where there are N

_{A}volunteers carrying out the activity in a time t

_{A}, which is the statistic distribution of time to perform all the actions contained in the entry control phase. Module 4 is the decision module, where the probability that a patient can be rejected because the body temperature is higher than 37.5 °C is P

^{temp}. If the temperature is normal, the patient flows through modules 5 and 6 which represent phase B. Module 5 is the queue of phase B and, thus, it contains the parameter Q

_{B}, while module 6 is the activity and is characterized by the time t

_{B}and the number of check-in operators N

_{B}. Then, a second decision module (module 7) appears with a probability P

^{fill-in}of having already filled in the forms. If it is false, the patient proceeds to module 8, which represents phase C (forms fill-in). In this module, the parameter Q

_{C}represents the maximum number of places to dedicate to the forms fill-in because phase C does not have any queue. The other parameters of module 8 are the duration of the activity t

_{C}, and the number N

_{C}of volunteers allocated to this phase. If the patient has already filled in the forms, he/she proceeds to phase D, contained in modules 9 and 10. As for the other phases, the former module is the queue, whose parameter Q

_{D}represents the maximum number of places in the queue to dedicate to phase D, while the latter is the performance itself, characterized by the duration t

_{D}, which changes if the health conditions are ok or not, and the number of resources N

_{D}. The third decision module (module 11) manages the rejection due to health conditions and contains a probability that the values of the anamnesis are all good P

^{anam}. If the condition is not satisfied, decision module 12 defines the probability P

^{rej}to be rejected because some negative conditions do not affect the vaccination. Patients admitted to the vaccination flow through phase E. Here, they wait in module 13, characterized by Q

_{E}, and then are processed in module 14, defined by duration t

_{E}and number of nurses N

_{E}. After the inoculation phase, patients must wait for possible side effects for an aleatory time t

_{F}in module 15. This can be considered as a queue with Q

_{F}the maximum number of places to dedicate for the waiting. Module 15 is linked to the decision module 16 that manages possible side effects which can occur with a probability P

^{eff}. If the condition is true, modules 17 and 18 represent the side-effects treatment phase, with Q

_{G}as maximum number of patients in queue, t

_{G}as the duration of the performance and N

_{G}as the number of doctors staffed. Time t

_{G}varies according to the fact that the patient shows real side effects or is just scared. Otherwise, patients exit the system through module 19. From module 14 the forms flow starts and reaches the module 20 which represents the registration of the information in the informatic system. The activity is performed by N

_{H}administrative operators in a time t

_{H}.

^{pat/nurse}). This parameter gives a measure of the system efficiency because it relates the number of people vaccinated with the number of resources available. In addition, the total number of patients vaccinated in a day (N

^{pat}) is a relevant measure to study the capacity of the system. Two time-related output indicators are the average and maximum time spent in the system (T

^{sys-avg}and T

^{sys-max}) and in the queue (T

^{wait-avg}and T

^{wait-max}) by each patient. These values give us an idea of the speed of the process and the percentage of the time lost for non-value-added activities. Finally, the third group of output parameters is the resources utilization (U

_{i}, with i = phase of the process) which reflects both the effort in using the minimum number of resources and the avoidance of resource overutilization to reduce employee’s burnout and unsatisfaction. All these outputs are summarized in Table 2.

#### 4.2. Digital Technology

## 5. Case Study

^{fill-in}which is higher for adults since they are more used to technology and are likely to print the form at home. As argued before, the model needs real data to be reliable and, thus, researchers have visited several clinics for flu vaccination, in October and November 2020, to collect many measurements on those parameters that could be useful for the COVID-19 vaccination too. For each phase, about 100 time-related values were measured which are then inserted in a data-fitting software to find the statistical distribution that better represents these data. Researchers also collected measures of the time between two consecutive groups’ arrivals, and Table 3 shows the distribution for each time parameter in seconds. In particular, there are three main distributions that represent these time-measures: the triangular distribution (TRIA), the gamma distribution (GAMM) and the Weibull distribution (WEIB). From the process observation and the conversation with the clinic’s managers, the probability measures are defined and inserted in the simulation model (Table 4).

## 6. Results

^{arrival}and the number of resources (N

_{i}), both medical and non-medical. The time between two consecutive arrivals ranged between TRIA(54,127,540) and TRIA(42,99,420), with a step of 7-s decrease in the mean value. For the number of resources, researchers started from the maximum number of resources feasible inside the defined layout and reduced this number until the system deteriorated. In particular, the number of non-medical employees varied from 22 to 14 while the medical personnel varied from 22 to 18. Thus, combining all these different possibilities, the total number of tested scenarios was 225. Many scenarios were tested because a larger number of resources does not result in a more efficient system, but a balanced integration of the different kind of resources is necessary. For example, if the maximum number of doctors is chosen, the anamnesis control phase will become very fast and this creates a bottleneck in the following phase (vaccine inoculation). Thus, the objective is to find the right number of doctors according to the other resources. From the 225 scenarios, the best five scenarios selected are the ones that maximized the main parameter N

^{pat/nurse}and are compared to find the optimal (Table 5). This scenario has the highest value of N

^{pat/nurse}but it is also feasible. To be feasible, the solution must respect layout boundaries related to the maximum number of people allowed in the queue or chairs dedicated for the forms fill-in and for the waiting after the inoculation. After a study of the layouts available, this total number was set to 310 places. Each of these five scenarios has some strengths and weaknesses. The first respects all the layout boundaries, has accepted values of U

_{i}, but, since it has high interarrival time, fewer patients are vaccinated. The second scenario has the same interarrival time distribution of the third scenario but it needs one more nurse and so it is less efficient in terms of patients vaccinated by each nurse. The fourth and last scenarios would be the best, according to the N

^{pat/nurse}indicator, but they exceed the layout boundaries and so they are not feasible. In addition, the fifth scenario overutilizes the anamnesis, inoculation, and registration resources because the value of U

_{i}is higher than 85%. Thus, the best scenario among those considered was the third one because it maximized N

^{pat/nurse}, respecting the space limit. This configuration increases the sustainability of the system both socially, with an acceptable workload for the operators, and economically, because the target number of patients is vaccinated in the least number of days and with the most efficient use of resources. This reduces costs due to the center opening and due to the workers’ salary.

^{pat/nurse}which represents the efficiency of a clinic. In detail, the value of this indicator is 18.03 patients vaccinated/hour per nurse, which means that, if we suppose a 10-h shift, each nurse vaccinates about 180 people each day. This is a very high value that is combined with other KPIs such as the total number of patients vaccinated every day (N

^{pat}) which is equal to 2164 for this best configuration. Other parameters are time-related, such as the average time in system (T

^{sys-avg}), which is 25 min, and the average time in queue (T

^{wait-avg}), which is 5.4 min. This means that just 20% of the time spent by a patient in the system is expended in non-value-added activities. These two measures are also computed for their maximum values to understand the worst-case scenario. To conclude, the third set of output parameters is the resources utilization (U

_{i}) that stays under 85%, which can be considered as a limit besides which employees are overutilized and burnout or unsatisfaction phenomenon can arise (Table 6).

- Duration of each phase for each patient and average durations.
- Timestamps of the beginning and the end of each phase.
- Number of patients in each queue in every minute.

^{pat}and N

^{pat/nurse}indicators. The second table shows the number of patients processed by each single resource and it is important to understand if some resources are more exploited than others during a working day.

## 7. Conclusions

^{pat/nurse}) because it gave a measure of the system efficiency. The best configuration found included 31 total resources, 18 of which medical, and provided a N

^{pat/nurse}equal to 18 patients vaccinated by each nurse every hour. This high efficiency allows dedicating a smaller space which leads to lower waste and energy consumption. After the definition of the static ideal clinic, the model was expanded with a smartphone application that helped to digitalize the entire process and change it dynamically. The application is based on NFC technology, where operators have an NFC reader (a smartphone) and each patient has an NFC tag (a badge) that is read by the smartphone for the entire duration of an activity. These durations are then sent to the data analysts to be managed. Through this application, researchers were able to collect time measures in real time from the physical system, analyze them to find the drawbacks of this system, run the virtual model, and translate the improvements found in the physical clinic, creating a typical digital twin. Because it is still in a preliminary state, this digital twin developed was tested in a small POD but it gave different improvement cues as well. Indeed, the outcomes of the digital twin suggested a dynamic shift between nurses and doctors to deal with both the huge queue before the inoculation phase at the beginning of the day and the high doctor utilization during the entire day.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**(

**a**) Main screen of the mobile app, with the 3 possible activities; (

**b**) 3 screens of the reading part where the planner defines the process and the phase and activates the reading.

**Figure 8.**First section of the dashboard. (

**a**) Plot of the number of people in queue before the inoculation phase at every minute; (

**b**) Plot of the number of people in queue after the inoculation phase at every minute; (

**c**) Plot of the number of people in the entire system at every minute.

**Figure 9.**Second section of the dashboard. (

**a**) the histogram reports the average number of people in queue in each phase; (

**b**) the histogram reports the maximum number of people in queue in each phase; (

**c**) the histogram reports the average time that a patient spends in queue for each phase; (

**d**) the histogram reports the maximum time that a patient spends in queue for each phase.

**Figure 10.**Third section of the dashboard. The histogram shows the average and the maximum time in system spent by each patient.

**Figure 11.**Fourth section of the dashboard. The histogram shows the resources utilization in percentage.

**Figure 12.**Fifth section of the dashboard. (

**a**) Table with all the most relevant KPIs, such as N

^{pat}and N

^{pat/nurse}; (

**b**) Table that shows the number of patients processed by each resource.

Name | Symbol | Units of Measure |
---|---|---|

Group size | S^{group} | patients |

Probability of a specific group size | P^{group} | % |

Inter-arrival time | t^{arrival} | sec |

Probability of having a body temperature lower than 37.5 °C | P^{temp} | % |

Probability of having already filled-in the forms at home | P^{fill-in} | % |

Probability that the anamnesis is completely ok | P^{anam} | % |

Probability of being rejected because of the anamnesis | P^{rej} | % |

Probability of experiencing side effects | P^{eff} | % |

Working time of a specific phase i | t_{i}i = A, …, H | sec |

Number of resources needed in a specific phase i | N_{i}i = A, …, H | resources |

Number of places to dedicate in queue for a specific phase i | Q_{i}i = A, …, H | places |

Name | Symbol | Units of Measure |
---|---|---|

Number of patients vaccinated per hour per nurse | N^{pat/nurse} | Patients/nurse × hour |

Number of patients vaccinated per day | N^{pat} | Patients/day |

Average time spent in the system by a patient | T^{sys-avg} | min |

Maximum time spent in the system by a patient | T^{sys-max} | min |

Average time spent in queue by a patient | T^{wait-avg} | min |

Maximum time spent in queue by a patient | T^{wait-max} | min |

Resource utilization for each phase i | U_{i}i = A, …, H | % |

Time-Related Parameter | Statistical Distribution [s] |
---|---|

t^{arrival} = time between 2 consecutive arrivals | TRIA(51,120,510) |

t_{A} = working time of entry control phase | 7 + WEIB(17.2, 1.03) |

t_{B} = working time of check-in phase | 6.5 + GAMM(6.27, 2.22) |

t_{C} = working time of forms fill-in phase | 54 + WEIB(73.6, 1.15) |

t_{D} = working time of anamnesis control phase | OK: 24.5 + WEIB(19, 1.54) NOT OK: 32 + WEIB(24.4, 1.51) |

t_{E} = working time of vaccine inoculation phase | 67 + GAMM(21.7, 2.12) |

t_{F} = waiting time after the inoculation | TRIA(480,780,960) |

t_{G} = working time of side effects treatment phase | REAL EFFECTS: TRIA(240,420,600) FEAR: TRIA(60,120,180) |

t_{H} = working time of registration phase | TRIA(42.5,75.5,122) |

Probability Parameter | Value [%] |
---|---|

P^{temp} = Probability of having a body temperature lower than 37.5 °C | 99 |

P^{fill-in} = Probability of having already filled-in the forms at home | 60 |

P^{anam} = Probability that the anamnesis is completely ok | 30 |

P^{rej} = Probability of being rejected because of the anamnesis | 5 |

P^{eff} = Probability of experiencing side effects | 5 |

PARAMETERS | SCENARIOS | |||||
---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | ||

Triangular coefficients for interarrival time [s] | A | 54 | 51 | 51 | 48 | 42 |

B | 127 | 120 | 120 | 113 | 99 | |

C | 540 | 510 | 510 | 480 | 420 | |

Number of resources (N_{i})i = A, …, G or i = “Exit control” | A- Entry control | 4 | 4 | 4 | 4 | 4 |

B- Check-in | 3 | 3 | 3 | 3 | 3 | |

D- Anamnesis Control | 4 | 4 | 4 | 4 | 4 | |

E- Vaccine Inoculation | 12 | 13 | 12 | 12 | 13 | |

H- Registration on PC | 6 | 6 | 6 | 6 | 6 | |

G- Side effects treatment | 2 | 2 | 2 | 2 | 2 | |

Exit control | 2 | 2 | 2 | 2 | 2 | |

Num tot medical resources | 18 | 19 | 18 | 18 | 19 | |

Num tot non-medical resources | 15 | 15 | 15 | 15 | 15 | |

NUM TOT RESOURCES | 33 | 34 | 33 | 33 | 34 | |

Resource utilization (U_{i})i = A, …, G | A- Entry control | 33.8% | 36.5% | 36.3% | 38.1% | 44.0% |

B- Check-in | 38.1% | 41.2% | 40.8% | 42.9% | 49.5% | |

D- Anamnesis Control | 71.6% | 77.4% | 76.6% | 80.4% | 91.8% | |

E- Vaccine Inoculation | 75.0% | 74.7% | 80.2% | 84.1% | 88.4% | |

H- Registration on PC | 71.6% | 77.4% | 76.5% | 80.5% | 91.4% | |

G- Side effects treatment | 19.4% | 22.6% | 21.9% | 23.2% | 25.4% | |

Time [min] | T^{sys-avg} | 23.7 | 23.9 | 25.1 | 26.4 | 32.8 |

T^{sys-max} | 52.7 | 59.3 | 60.9 | 64.1 | 97.3 | |

T^{wait-avg} | 4 | 3.4 | 5.4 | 5.9 | 12.4 | |

T^{wait-max} | 38.4 | 44.3 | 48 | 56 | 83.4 | |

Number of places to dedicate in the layout (Q_{i})i = A, …, G | A- Entry control | 26 | 32 | 25 | 27 | 43 |

B- Check-in | 29 | 30 | 30 | 29 | 33 | |

D- Anamnesis Control | 101 | 136 | 116 | 143 | 320 | |

E- Vaccine Inoculation | 43 | 17 | 64 | 74 | 20 | |

F- Waiting post Inoculation | 66 | 68 | 67 | 67 | 70 | |

G- Side effects treatment | 3 | 4 | 4 | 3 | 3 | |

Num tot places in the layout | 268 | 287 | 306 | 343 | 489 | |

N^{pat} | 2026 | 2192 | 2164 | 2270 | 2567 | |

N^{pat/nurse} | 16.9 | 16.9 | 18.0 | 18.9 | 19.8 |

Output Parameter | Value | Units of Measures |
---|---|---|

N^{pat/nurse} | 18.03 | Patients/nurse × hour |

N^{pat} | 2164 | Patients/day |

T^{sys-avg} | 25.1 | min |

T^{sys-max} | 60.9 | min |

T^{wait-avg} | 5.4 | min |

T^{wait-max} | 48 | min |

U_{A} | 36.3 | % |

U_{B} | 40.8 | % |

U_{D} | 76.6 | % |

U_{E} | 80.2 | % |

U_{G} | 21.9 | % |

U_{H} | 76.5 | % |

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**MDPI and ACS Style**

Pilati, F.; Tronconi, R.; Nollo, G.; Heragu, S.S.; Zerzer, F.
Digital Twin of COVID-19 Mass Vaccination Centers. *Sustainability* **2021**, *13*, 7396.
https://doi.org/10.3390/su13137396

**AMA Style**

Pilati F, Tronconi R, Nollo G, Heragu SS, Zerzer F.
Digital Twin of COVID-19 Mass Vaccination Centers. *Sustainability*. 2021; 13(13):7396.
https://doi.org/10.3390/su13137396

**Chicago/Turabian Style**

Pilati, Francesco, Riccardo Tronconi, Giandomenico Nollo, Sunderesh S. Heragu, and Florian Zerzer.
2021. "Digital Twin of COVID-19 Mass Vaccination Centers" *Sustainability* 13, no. 13: 7396.
https://doi.org/10.3390/su13137396