Simulation modeling assessment and improvement of a COVID-19 mass vaccination center operations

1. Introduction

The COVID-19 pandemic has imposed many lockdowns over the past 2 years, resulting in negative consequences on human, social, and especially economic aspects.^1–3 The global efforts to develop an effective solution to counter this pandemic have led to the invention and validation of several effective vaccines.^4–6 However, vaccine development is only the first phase of the COVID-19 vaccination process. Indeed, all countries have to move on to implement rapid mass vaccination. The success of any mass vaccination program depends on getting the vaccine to people quickly and efficiently. Especially, since this vaccination program must take place in a healthcare system overloaded by COVID-19 positive cases. Social distancing constraints must therefore be considered. Hence, this vaccination program requires extraordinary amounts of planning and preparation at various levels. Planning and preparation include vaccination priorities, vaccine delivery methods, public outreach, and vaccination center design and management.

Discrete event simulation (DES), characterized by its high flexibility and speed, has been used to model, analyze, and evaluate the efficiency of hospital and public health infrastructures.^7–11 In this context, various researchers used the DES to build and manage mass vaccination centers. Washington ¹² evaluated the design and performance of an actual mass vaccination center operated by the Henderson County Public Health Department in North Carolina, USA, during the pandemic of influenza/pneumococcal. In his study, the author classified the person into three categories: those receiving a free vaccine, which had to pay to receive a vaccine, and with special needs. Special needs persons received the free vaccine but need help to move around the center. The vaccination circuit for free and special needs persons goes through three steps: taking a copy of the insurance card, registration, and vaccination against influenza. The vaccination circuit for the persons who had to pay for their vaccines goes only through the two steps of payment and vaccination. Besides the influenza vaccine, people have the option to be vaccinated against pneumococcal. Here, these persons have to register again. Based on the collected data, the author developed and validated a DES model to measure the throughput of the vaccination center. Next, the author examined its effectiveness as a function of increased vaccine arrivals. Finally, the author determined the optimal center layout using a simulation-optimization tool to allow the vaccination of a maximum number of persons per day. The results showed that the new center layout improved the vaccination rate in the center while minimizing the number of staff, but this resulted in long waiting times. In addition, the simulation results reported a high operating cost in both original and optimized vaccination center models.

Gupta et al. ¹³ designed and built a DES model of a drive-through mass vaccination center in Louisville, Kentucky, in 2009 during the H₁N₁ pandemic. The flow in the drive-through vaccination center follows three steps: the consent form handout, the consent form fill-in, and the vaccination. At the first step of the drive-through center, each individual in an arriving vehicle receives a consent form to fill out. After receiving the consent form, all the people fill them out. Then, this vehicle goes to the vaccination step. After receiving the vaccine, it either leaves the system or takes a detour that allows person that may experience some after-effects of the vaccination to be examined by a doctor. The authors examined the effect of different factors on center performances, such as the average number of vehicles in the center, the average number of waiting vehicles, the average vehicle’s time in the system, the average vehicle’s time in the queue, and the worker utilization. The considered factors were the number of arriving vehicles, the number of consent form lanes, the number of consent form workers per lane, the length of a consent form lane, the number of vaccination lanes, the number of medical workers per lane, and the vaccination lanes length. The authors examined two simulation scenarios in their study. In the first one, they compared the DES model results with the real center’s data to validate the simulation model and to study the effects of the considered factors on the measured performance. Results showed that for a fixed length of vaccination lane and consent form, an increase in the number of consent form workers per lane had much more impact than increasing the number of medical workers per lane. Indeed, it reduces the average time in the system and increases the total number of vaccinated person. In the second scenario, the authors simultaneously studied the interactions among several factors using a simulation-optimization tool. They determined the required number of points of dispenses lanes, the number and length of consent handouts and fill-in lanes, and the needed staff at the consent handout stations and points of dispenses to minimize the average user waiting time in the system. This study suffers from a weakness in the statistical analysis of the simulation results. Indeed, although the authors relied on confidence intervals to present the performance measures collected in the different studied scenarios, they performed no statistical analysis to compare these results. Such a comparison could have altered the conclusions of this study.

Beeler et al. ¹⁴ developed a DES model of a Canadian mass vaccination center during the 2009 H₁N₁ pandemic in Ontario. The individuals arrive at the vaccination center without a prior appointment and must wait outside if the center is not yet open or if it is at maximum capacity. Some persons may be put off by the size of the queue at the center and choose to leave, or others may reconsider their decision to be vaccinated if they have waited too long. The authors developed and validated the simulation model based on a baseline scenario with observed staffing levels and patient demand from three vaccination days at a mass vaccination center. Next, they used a full design of experiments to investigate the influence of several factors on total vaccination volume, individual waiting times, operating costs, and the risk of influenza transmission at the center. The considered factors were priority access restrictions, nurse staffing number, registration clerk staffing number, number of operation hours, and infection and patient arrival rates. Analysis of the variance of the simulation results showed that most of the studied factors and some first-order interactions between them had statistically significant effects on the considered performance measures. In addition, the simulation results showed that making vaccination center staffing decisions based on meeting vaccination targets without the costs associated with long waits or the possibility of internal infection risk could lead to underinvestment in the centers. Besides reducing waiting times adding staff under the right circumstances also modestly reduces the number of intra-facility infections. Analysis of staff productivity data revealed that it would be possible to increase patient throughput in centers without adding staff.

Recently, Asgary et al. ¹⁵ developed DES models to improve the planning, design, operation, and feasibility of a drive-through mass COVID-19 vaccination in Denver, Colorado, USA. The predetermined site for this mass vaccination center was the parking of a baseball stadium. This site was large and long enough to accommodate up to 10 lanes of traffic with sufficient space between them. In addition, it connected to wide streets and highways for easy ingress and egress of cars. The authors developed two different simulation models based on the sketches provided by the health authorities. In the first model, cars can enter one of six available check-in lanes and proceed to one of three vaccination tents connected to their check-in lane. Four staff members at each check-in station and two vaccinators at each vaccination station make it possible to simultaneously check-in and vaccinate four and two people. In the second model, entering cars choose one of eight lanes and undergo registration and vaccination simultaneously. Four stations in each lane could serve patients. However, patients with special needs or those requiring more time go to peripheral tents to minimize potential delays. The authors based their analysis on the number of served cars during an 8-h vaccination day in addition to the average treatment times per car. The results showed no significant difference between the two models’ number of processed cars. Nerveless, we note that the developed models were no-stochastic, which explains the lack of substantial difference between the simulation results. Indeed, all the used service times were constant. In addition, the second model had a lower overall average processing time than the first. This result is expected, given the higher number of vaccination lanes in this second model. To analyze the sensitivity of the simulation models, the authors examined the effects of variations in the rate of car arrival on the number of treated cars and the average treatment time. The results showed that the second model processes more cars than the first. Again, these results were predictable, given the difference in the number of vaccination lanes in the two conceptual models of the vaccination center.

Wood et al. ¹⁶ investigated the effect of computer modeling and simulation on the establishment of COVID-19 vaccination centers at two regional vaccination centers, A and B, in southwest England in the early days of the mass vaccination effort in the United Kingdom. In center A, the flow of vaccination follows the registration, clinical assessment, vaccination, and observation steps. Center B combined the two clinical assessment and vaccination steps. The authors fit various statistical distributions to sample the service time’s data. Next, they modeled vaccination center activities using a DES tool. It was then possible to quantify the number of daily bookings at center A. The authors also revealed how the analysis enabled a significant operational change by combining two activities in the vaccination pathway into one at center B. The comparisons between the patient throughput in this center and center A resulted in center B’s superiority. Finally, they examined the operational resilience of center B by simulating potential shocks to the pathway as arrival delays and staff unavailability. The simulation results highlight that the assignment of people arrivals is not sustainable. In effect, a bottleneck forms in the vaccination activity.

A part of these studies took place in a different context than the COVID-19 pandemic or based on a drive-through structure. Developing countries cannot use this structure, as most of their populations do not have vehicles. In addition, most of these studies focused on maximizing the number of vaccinated persons per center. Undoubtedly, maximizing this number would optimize any mass vaccination campaign by reducing the required days. However, the contagious nature of the COVID-19 virus requires authorities to impose strict distancing measures within vaccination centers. To comply with these measures, it would be first necessary to consider the waiting time of individuals and the number of persons waiting in the center. Furthermore, several studies did not consider the variability of person arrivals to the center. All these shortcomings are the leading motivations for the present work. In this paper, we assessed the control of a walk-in COVID-19 mass vaccination center in the Tunisian city of Sfax using modeling and simulation.

Our main aim is to provide the public health authorities with information on the likely impact of changes in the center’s layout on several of its performance measures as the average waiting time per person at the center to be vaccinated, the number of persons present at the center, and other performance measures under different arrival time scenarios. As a secondary aim, we were interested in the possibility of increasing the total number of vaccinated persons in the center. The structure of this article follows five sections. We provide in the second section the background on the Tunisian vaccination strategy. In the third section, we present the stages of the simulation models development method. In this section, we first define every task undertaken during the vaccination process. Then, we describe service times and data analysis processes besides the adopted arrival rates of persons to the vaccination center. In section 4, we describe and discuss the main simulation results. Section 5 summarizes and discusses future works.

2. Background

On 17 March 2021, Tunisia received the first batch of 93,600 doses of Pfizer COVID-19 vaccine as part of the global COVAX initiative. ¹⁷ This delivery was part of a first wave of vaccine arrivals to vaccinate 20% of the population in Tunisia. Tunisian health authorities considered the risk of complications and mortality by age group to establish the vaccination order of priority for the population. This order is dynamic and may be revised based on the availability of vaccines. To target priority groups, the Tunisian health authorities have set up a national vaccination registration campaign. The registrant database guarantees a vaccination appointment for each registered person. It also distributes the persons to the vaccination centers according to the prioritization criteria (age, pre-existing disease, and risk exposure). An SMS is sent to each person, providing the registration number, the date and time slot, and the vaccination center. For the second injection, if needed, another SMS is sent back with the new information. ¹⁸

3. Methods

We used the Arena Rockwell DES software to develop the different simulation models of the vaccination center. Each one of these models has a physical layout and uses several operators that interact with the flow of entering persons to the center based on pre-defined logic.

3.2. Analysis of service times data

No data on the service times in the center was available. Indeed, the health authorities only collected the statistic on the total number of vaccinated persons. Hence, researchers with student volunteers conducted time observation to collect center service time data. They measured the duration of each vaccination task in the center several times.

The observations were conducted during 5 days of vaccination center operation. The number of observations differed from one stage of the vaccination process to another depending on the availability of observers and the ease of observation (Table 1). All the collected empirical measures were then processed to fit the task durations to various statistical distributions using the input analyzer tool (Table 1). This tool is a standard component of the Arena Rockwell software environment that can fit distribution functions to empirical data. For the “Observation” task, the adopted time is constant and equal to 15 min.

OPEN IN VIEWER

Table 1.

Service times parameter values and resulting distributions.

Task
Registration and allocation of waiting number		Number of observations	704
		Expression	3.5 + GAMM (8.43, 1.13) (in seconds)
		Distribution
Pre-vaccination check		Number of observations	416
		Expression	16.5 + LOGN (24.1, 22.4) (in seconds)
		Distribution
Vaccine preparation and injection	Preparation and injection	Number of observations	462
		Expression	7 + WEIB (24.7, 1.12) (in seconds)
		Distribution
	Multi-dose vial recovery from pharmacy	Number of observations	70
		Expression	35 + EXPO (81.9) (in seconds)
		Distribution
Validation		Number of observations	352
		Expression	11.5 + ERLA (7.35, 2) (in seconds)
		Distribution

GAMM (α, β): Gamma distribution with shape parameter “α” and the rate parameter “β”; LOGN (µ, σ): Lognormal distribution with mean “μ” and standard deviation “σ”; WEIB (α, β): Weibull distribution with the shape parameter “α” and the scale parameter “β”; EXPO (µ): Exponential distribution with mean “µ”; ERLA (µ, k): Erlang distribution with mean “µ” and erlang order parameter “k.” Table showing the number of observations, the expression of the statistical distribution, and the distribution graph for each operation in the vaccination center.

The collected data may be subject to some inaccuracies due, in part, to the limited number of observers, time, and equipment available to conduct the time study. Nevertheless, the data sufficed to build a valid simulation model.

3.3. Arrival rates

The arrivals rates were based on different scenarios (Figure 1). In the first one, theoretical arrivals rates were based on regular appointments from 8.30 am to 5 pm. Appointment arrival times were given at a rate of 90 persons per half hour. The arrivals between two appointments were therefore scheduled stochastically, as long as the condition of 90 arrivals in total was met. In the second scenario, hypothetical arrivals are based on the same appointment schedule with some random noise, reflecting that most people would turn up at their allotted time, while a smaller proportion would arrive after their allotted time. However, all the scheduled 90 persons for each appointment arrive between two successive appointments. In the last scenario, real arrivals are scheduled with significant random noise. In this scenario, most of the persons arrive at the beginning and middle of the day. This scenario reflects that most scheduled persons are aged and require an attendant who, in most cases, works during the day.

OPEN IN VIEWER

Figure 1.

The three studied scenarios of person arrival rates. Histograms showing arriving persons during the day at the vaccination center according to the three theoretical, hypothetical, and real scenarios.

3.4. Vaccination center models

Two simulation models of the vaccination center were developed using Arena software. The first model represents the actual operating mode of the center. The second model represents our proposal for the improvement of the center.

3.4.1. Actual vaccination center model

The flow of persons in the vaccination center is managed according to the following pathway (Figure 2).

OPEN IN VIEWER

Figure 2.

Actual mass vaccination flow model. Diagram of the flow of persons through the different stations in the actual model of the vaccination center, grouped into the four zones: registration, pre-vaccination check, vaccination/validation, and observation.

Persons who arrive at the center must wait in the queue in front of the Registration station to receive a waiting number. Later, they are sent to the waiting area until one of the pre-vaccination check queues stations becomes empty. Here, the first waiting six persons move to this queue. It was observed that at least 2% of persons who take this pre-vaccination check would not be eligible to receive the vaccination because of a suspected allergy to the vaccine. Hence, they are dismissed and will pass a more advanced check-in at a specialized institution for further verification. The accepted persons are placed on hold until a vacancy occurs in one of the three vaccine boxes. The capacity of each box is limited to six people. An arriving person at one vaccination box passes through the validation station to receive the validation SMS. Then he moves to the vaccination station to receive the vaccine. Finally, he moves to the observation section, where he is placed under medical surveillance to check his health.

Three volunteers are assigned to the registration station, two volunteers and two health care providers to the four pre-vaccination check stations, one volunteer plus two health care providers to each one of the three vaccination boxes, and one doctor for the observation area and the pre-vaccination check stations. Hence, 17 staff members, including volunteers, health care providers, and doctors, are required to run this vaccination center model.

3.4.2. Proposed vaccination center model

In our proposal vaccination model, we rearrange the vaccination steps in a different order to relieve the congestion in the center. In addition, we adjust the staff assignments and add a fourth vaccination box to ensure the respect for social distancing constraints (Figure 3).

OPEN IN VIEWER

Figure 3.

Proposed mass vaccination flow model. Diagram of the flow of persons through the different stations in the proposed model of the vaccination center, grouped into the four zones: registration, pre-vaccination check/vaccination, validation, and observation.

First, we released the two health providers assigned to the pre-vaccination check task in the previous model and reassign them to a new vaccination box. Hence, the total number of vaccination boxes was increased to four. In addition, we attribute the pre-vaccination control task only to four volunteers, each one of them allocated to a vaccination box. The validation task is moved outside the vaccination boxes to relieve the congestion. This task is grouped into one desk located after the vaccination boxes. Second, to respect the social distancing constraint, we divided the common waiting area of the previous center model into four areas in our proposed model. Each area is specific to one of the four vaccination boxes. Finally, we assigned two volunteers to the registration task. The 17 center’s staff members are hence reassigned so that there are two volunteers in the registration task, one volunteer plus two health care providers in each of the four vaccination boxes, two volunteers in the validation task, and one doctor for the observation area. The number of required operators for our proposed model remains the same as the actual one while having the possibility of adding another vaccination box. The flow of persons follows the same steps as the actual model, but in a different order. Every person entering the center must wait in the queue in front of the registration station to receive a number. Then he is oriented to the waiting area with the lowest number of waiting persons. Each time a person leaves one of the vaccination boxes, the first person in its waiting area is selected, knowing that each of the four vaccination boxes can only accommodate a maximum of six persons at a time. This person passes through the pre-vaccination checkpoint and then to the vaccination station. The vaccinated persons leave the vaccination boxes and move to the validation station. Finally, they move to the observation area.

4. Simulation results and discussion

To collect the simulation results, each model is simulated under the three scenarios for 30 replications of 510 min each. Each replication starts with an empty center with no warm-up period. All the results are provided in Appendix A. The adopted performance metrics are

The first performance measure is used to validate the simulation model while the other four are used to assess and improve the mass vaccination center.

4.1. Simulation model validation

To determine whether the simulation model as constructed accurately represents the real system, the results of this system are compared to the simulated model results. The mass vaccination center uses only the total number of vaccinated peoples per day as statistics. Hence a Student’s t-test is applied to determine whether the difference between the total number of vaccinated people per day at the mass vaccination center and the simulation model, with the real arrivals scenario, was significant or not. The t-test is employed at a 5% significance level with the following hypothesis:

H 0 : Difference = NOU T center − NOU T simulation = 0

(1)

H 1 : Difference = NOU T center − NOU T simulation ≠ 0

(2)

As shown in Figure 4, the difference between NOUT_center and NOUT_simulation is between −21.960 and 28.360 at the 95% confidence level. With a p value of 0.8, the results of the t-test reveal this difference is not significant at the 0.05 level of significance. Therefore, the simulation model is validated.

OPEN IN VIEWER

Figure 4.

Comparison of center and simulation model results. Figure showing the graphical plots of 30 observations of the number of vaccinated persons by the real center and the current simulation model of the vaccination center with the real arrivals scenario. It shows through a student’s t-test and the estimation of the confidence interval of the difference between these two numbers that it is not significant.

4.2. The average total number of vaccinated persons on time versus the average total number of arrival persons (ANOUT/ANAR)

This ratio measures the percentage of persons who receive the vaccine on time to evaluate the efficiency of the vaccination center under different arrival scenarios. Simulation results show that in both models, and for all the arrival scenarios, most arrival persons receive the vaccine on time (Figure 5).

OPEN IN VIEWER

Figure 5.

Number of vaccinated persons on time versus number of arrivals (in person). Graphs of the number of persons arriving at the center and the number of vaccinated persons in the current and proposed center models for the three arrival scenarios.

Figure 6(a) displays 95% confidences interval (CI) for the ANOUT/ANAR ratio of all the simulation models with the three arrivals scenario. This figure corroborates the previous result. Indeed, in the actual model, the mean rate of persons who received the vaccine dose in time for the theoretical, hypothetical, and actual arrival scenarios is 93.95%, 94.90%, and 97.34%, respectively. With the proposed model, the values of this rate are equivalent to those of the actual model. Indeed, they are 94.55%, 95.87%, and 97.50%, respectively. In addition, this figure shows a significant difference between the results of the two simulation models for all the arrival scenarios except the real arrival one. Indeed, the CI for the actual model ANOUT/ANAR does not overlap the CI for the proposed model ANOUT/ANAR for the two first arrival scenarios. And t-tests confirm this analysis (Figure 6(b)–(d)).

OPEN IN VIEWER

Figure 6.

The ANOUT/ANAR analysis. Figure showing the confidence intervals of ANOUT/ANAR for the current and proposed models of the vaccination center for the three arrival scenarios. It shows the result of the comparison by student’s t-test and the confidence interval of the difference between the ANOUT/ANAR of the current and proposed models of the vaccination center for the three arrival scenarios.

It is worth mentioning here that the remaining unvaccinated persons are not accepted at the center because of ineligibility for the vaccine or vaccinated after the center’s operating hours. In the latter case, these persons are excluded from this ratio but considered in the total number of vaccinated persons in the center’s statistics.

4.3. The average total vaccination time per person (ATVT)

The total vaccination time is measured by subtracting the person’s exit time from the entry time to the center. It characterizes the fluidity of the person’s flow in the center (Figure 7).

OPEN IN VIEWER

Figure 7.

The total vaccination time per person (in minutes). Graphs plots of the total vaccination time per person in the current and proposed models of the vaccination center for the three arrival scenarios.

The ATVT in the actual model increases from 19.748 min for the theoretical arrivals to 24.002 min for the hypothetical arrivals and 33.839 min for the actual arrivals. In contrast, this average is almost comparable across the three arrivals for the proposed model. In fact, this average is equal to 17.401 min, 21.189 min, and 21.698 min for the three arrivals (Figure 8(a)). In addition, there is no overlap between the CIs for the ATVT of the actual model and the CIs of the proposed model for all arrival scenarios. The difference between the two simulation models is significant. T-tests confirm that the AWT of the actual and proposed model differs at the 0.05 level of significance for all the three scenarios (Figure 8(b)–(d)).

OPEN IN VIEWER

Figure 8.

The ATVT analysis. Figure showing the confidence intervals of ATVT for the current and proposed models of the vaccination center for the three arrival scenarios. It shows the result of the comparison by Student’s t-test and the estimation of the confidence interval of the difference between the ATVT of the current and proposed models of the vaccination center for the three arrival scenarios.

4.4. The average waiting time per person (AWT)

The waiting time per person is the sum of all the time spent by that person waiting during each step of the vaccination process (Figure 9).

OPEN IN VIEWER

Figure 9.

The waiting time per person (in minutes). Graphs plots of the waiting time per person in the current and proposed models of the vaccination center for the three arrival scenarios.

Both models of the vaccination center showed relatively acceptable AWT. Indeed, the averages of these times vary from 0.878 min with the proposed model for the theoretical arrival scenario to 17.321 min with the actual model for the real arrival scenario (Figure 10(a)). The difference between the AWTs of the two models is significant as no overlap between the CIs for the AWTs of the actual and proposed models was detected for the three arrival scenarios. T-tests confirm that the AWT of the actual and proposed model differs at the 0.05 level of significance for all the three scenarios (Figure 10(b)–(d)).

OPEN IN VIEWER

Figure 10.

The AWT analysis. Figure showing the confidence intervals of AWT for the current and proposed models of the vaccination center for the three arrival scenarios. It shows the result of the comparison by student’s t-test and the estimation of the confidence interval of the difference between the AWT of the current and proposed models of the vaccination center for the three arrival scenarios.

4.5. The average number of persons in the center (ANPI)

This measure verifies whether the social distancing condition necessary to limit the spread of COVID-19 is met. Indeed, the higher this number is, the more difficult it is to ensure this condition. Both models have high values of persons present in the center for all the studied arrivals scenarios (Figure 11). Indeed, the average value of this number varies between 51.716 and 100.510 (Figure 12(a)).

OPEN IN VIEWER

Figure 11.

The number of persons present in the center (in person). Graphs of the number of persons present in the current and proposed models of the vaccination center for the three arrival scenarios.

OPEN IN VIEWER

Figure 12.

The ANPI analysis. Figure showing the confidence intervals of the ANPI for the current and proposed models of the vaccination center for the three arrival scenarios. It shows the result of the comparison by student’s t-test and the estimation of the confidence interval of the difference between the ANPI of the current and proposed models of the vaccination center for the three arrival scenarios.

As with the previous performance measures, the difference between the ANPI of the two models is significant. Indeed, there is no overlap between the CI for the ANPI of the two models for the three arrival scenarios. This difference is most significant with the real arrivals scenario (Figure 12(a)). T-tests confirm that the ANPI of the actual and proposed model differs at the 0.05 level of significance for all the three scenarios (Figures 12(b)–(d)).

4.6. The average operator utilization rate (AUTIL)

This rate has not been used in other vaccination center simulation studies. We define it as the sum of the effective working time of each operator divided by the total time of a working day. The aim is to maximize this average to improve operator performance. This average rate varies from one station to another. In fact, while this rate remains low for the registration station, it reaches relatively high values for the validation station. The highest values reach 64.55% for this station in the proposed model simulated for the theoretical scenario of arrivals. This is because of the number of volunteers assigned to this post, as only two volunteers handle the registration task (Figure 13). T-test reveals that the total AUTIL of the actual and proposed model differs at the 0.05 level of significance for all three scenarios (Figure 14).

OPEN IN VIEWER

Figure 13.

95% CI for AUTIL. Figure showing the confidence intervals of the AUTIL for every task in the current and proposed models of the vaccination center for the three arrival scenarios.

OPEN IN VIEWER

Figure 14.

The total AUTIL analysis. Figure showing the confidence intervals of the total AUTIL for the current and proposed models of the vaccination center for the three arrival scenarios. It shows the result of the comparison by student’s t-test and the estimation of the confidence interval of the difference between the total AUTIL of the current and proposed models of the vaccination center for the three arrival scenarios.

4.7. Discussion

4.7.1. Center’s response to arrivals variability

The simulation results, for the three arrival scenarios, show that the two vaccination center simulation models respond well to the variability in person arrivals. Indeed, 93.95%–97.50% of arriving persons at the center receive the vaccine on time. In addition, the average total vaccination time does not exceed 33.839 min. This average time is reasonable and proves that the flow of persons in the center is fluid. Furthermore, the average waiting time is acceptable and remains less than or equal to 17.321 min.

The more complex problem of the center’s management is the social distancing condition respect. Indeed, the average number of persons in the center value is high and varies between 51.716 and 100.510 persons. The center’s spaces, especially waiting areas, must be well-sized and organized to respect the social distancing condition.

4.7.2. Comparison of the two vaccination center model’s results

The simulation results show that the percentages of persons who receive the vaccine on time in the two models are not equivalent with the theoretical and hypothetical arrivals scenarios. But with the real arrivals scenario, the two simulation models behave in equivalent ways. However, we note a superiority of the proposed model in terms of the number of people vaccinated in time, even if this superiority is minor in the scenario’s case of real arrivals.

This superiority, in favor of the proposed model, is very clear with the average total vaccination time per person for all three arrival scenarios. Indeed, this average time increases significantly from one arrival scenario to another in the actual model, while its increase in the proposed model is not as substantial. The difference between the proposed and the actual model average vaccination times is equal to 2.437, 2.813, and 12.141 min in favor of the proposed model for the theoretical, hypothetical, and real arrival scenario. In addition, the proposed model always generates lower average waiting times than the actual model for the three arrival scenarios. Indeed, this time decreases by 73%, 37.72%, and 70% in the proposed model for the theoretical, hypothetical, and real arrival scenarios compared with the actual model.

The simulation results also show that the average number of persons in the center increases from one scenario to another. However, this number increases more significantly in the actual model than in the proposed model. In fact, this average number increases from 58.555 persons for theoretical arrivals to 72.110 persons for hypothetical arrivals in the actual model. It, therefore, rises by 25.28%. It also grows by 71.65%, from 58.555 persons for theoretical arrivals to 100.51 persons for actual arrivals. While in the proposed model, the increase in this average number is not as substantial. In fact, it is equal to 22.33% and 24.65% when the scenario of arrivals changes respectively from theoretical to hypothetical and from theoretical to real.

The average utilization rate of all operators in the proposed model is more important than the average rate in the actual model. Indeed, in the actual model, this average rate is respectively equal to 41.95%, 41.63%, and 41.077% for the theoretical, hypothetical, and real scenarios of arrivals. With the proposed model, this rate is 46.47%, 46.55%, and 46.49%. The operators are hence slightly better used in the proposed model than in the actual one.

In summary, all the indicators show that the reorganization of the tasks of the vaccination center and the new mode of assigning operators in the proposed model generate better responses than those of the actual center. Nevertheless, the operator utilization averages of this proposed model need to be improved.

4.7.3. Improved performance of the proposed model

We explored opportunities to improve the performance of the proposed model. Hence, the number of arrivals was gradually increased in the proposed simulation model for the real arrivals scenario while measuring the average operator utilization rate and other performance measures. Nevertheless, various limitations were set:

A maximum average operator utilization rate AUTIL ≤ 90%.

An average number of persons in the center ANPI ≤ 200.

An average waiting time per person AWT ≤ 30 min.

An average total time for vaccination per person ATVT ≤ 60 min.

An increase in the number of arrivals by 36% generates the following simulation results (Table 2).

OPEN IN VIEWER

Table 2.

Proposed model results with increase in arrivals.

Performance measure	Mean	95% CI
ANOUT/ANAR	97.50%	(97.39;97.60) %
ATVT	42.35 min	(40.72;43.97) min
AWT	25.662 min	(24.07;27.25) min
ANPI	173.71persons	(165.52;181.91) persons
AUTIL	63.16%	(62.61;63.72) %

CI: confidence interval; ANOUT/ANAR: The average total number of vaccinated persons on time versus the average total number of arrival persons; ATVT: The average total vaccination time per person; AWT: The average waiting time per person; ANPI: The average number of persons in the center; AUTIL: The average operator utilization rate. Table showing the mean (column 2) and the 95% confidence interval (column 3) of the ANOUT/ANAR, the ATVT, the AWT, the ANPI, and the AUTIL of the proposed model of the vaccination center after a 36% increase in the number of arrivals of the real scenario.

The proposed vaccination center model can accept this increase under optimal operating conditions. Indeed, the ANOUT/ANAR ratio of this model remains in the same proportions as the same model without an increase in the number of arrivals. This number of arrivals can be handled by 17 operators composed of volunteers, health care providers, and doctor. Nevertheless, the average number of persons present in the center will be equal to 173.71 persons. It is, therefore, necessary to provide adequate space, especially in waiting areas, to respect the social distancing condition.

5. Conclusion and future work

This article focuses on the modeling and assessment of a mass vaccination center in the COVID-19 global pandemic. The studied center is one of the first vaccination centers established in the city of Sfax in Tunisia. First, observations were made for 5 days to acquire data on the center’s service times. For this, the duration of each vaccination task in the center was measured during this observation period. All the collected empirical measurements were then analyzed to fit the task durations to various statistical laws. Based on these statistical laws, simulation models of the vaccination center were finally developed through the ARENA tool to analyze and improve the operation of the center.

The primary aim of this study is to verify the response of the vaccination center to variability in arrivals. Hence, three scenarios of arrivals were simulated. The first one represents the theoretical scenario of arrivals on which the health authorities based their development of the actual center model. In this scenario, the center accepts 90 persons per half hour on appointment. In the second scenario, more realistic, the center always accepts 90 persons per half hour on appointment. However, most admissions are concentrated in the first 10 min of every half hour. The third scenario represents the reality experienced by the center’s staff. In this scenario, most persons do not respect their appointments. A large part of arrivals is concentrated at the beginning and the middle of the day. The simulation results showed that the actual center model responds well to the variability of arrivals.

For the second aim of this study, another model of the center was proposed and simulated to improve the performances of the center. Like the first model, this proposed model underwent the same evaluation process through the three arrivals scenarios. The simulation results show that the proposed model responds well to the arrival’s variability. In addition, this proposed model outperforms the actual one. Based on these results, a series of simulations were applied to the proposed vaccination center model to explore the effect of increasing the number of arrivals in the real scenario. The increase in the number of arrivals must respect acceptable operating limits. The fundamental limit was the operator utilization rate. These simulations made it possible to increase the number of arrivals by 36%. Beyond this value, the operator utilization rate exceeds the limits of feasibility.

In summary, both actual and proposed simulation models of the vaccination center model respond well to the variability of person arrivals. However, the proposed model performs better than the actual model. All indicators showed that the reorganization of the vaccination center’s tasks and the new assignment of operators in the proposed model give improved responses compared to the actual center. Indeed, the proposed model gives higher average total number of vaccinated persons on time versus the average total number of arrival persons and average operator utilization rate, and lower average total vaccination time per person, average waiting time per person, and average number of persons in the center than the actual model.

To our knowledge, this is the first article that assesses the management of a vaccination center in a developing country with no previous experience. It required significant effort to collect data, develop simulation models, and analysis results. Especially since health authorities did not collect any times data. The results derived from this study can be used by other researchers to develop future mass vaccination policies, especially in developing countries, as the world remains in the grip of the COVID-19 pandemic and may be subject to other pandemics in the future.

Many aspects of this study are currently being developed. The first aspect is the enlargement of the comparison scope to other vaccination center models. In the second aspect, multi-objective optimization methods will be investigated, to improve the performance measures of the center. Another extension of this work can be the integration of the proposed simulation model with a layout design tool to explore the center configuration that best fits the space. The third extension of our study is the investigation of the connectivity between multiple vaccination centers in the same city to better manage the variability of person arrivals.