Modelling of the Influence of the Peer Environment on the Prevention

of Caries Development in Schoolchildren using a Hybrid Simulation

Approach

Maria Hajłasz

and Bożena Mielczarek

Faculty of Management, Wrocław University of Science and Technology,

ul. Ignacego Łukasiewicza 5, 50-371 Wrocław, Poland

Keywords: Hybrid Simulation, Agent-based Simulation, Discrete Event Simulation, Dental Caries, Decision Support.

Abstract: Dental caries is a disease caused by medical and nonmedical factors. It can be prevented by taking conscious

preventive action. In addition to the services provided by dentists and dental hygienists, awareness is very

important in preventing the development of the disease. Awareness can be shaped, among other things, by

the environment of peers. The aim of this paper is to use a hybrid simulation to investigate the impact of

supportive, neutral, and non-supportive peer environments on strengthening or weakening the effectiveness

of dental caries prevention in students of a sample primary school in southwestern Poland. Three experiments

were carried out in which the effectiveness of preventive services varied. The effectiveness depended on the

individual approach of the students to oral hygiene and dietary habits. Depending on the frequency of

changing the closest peer environment, individual student attitudes change over time, which in turn affects

the effectiveness of preventive services. Hybrid simulation, which combines discrete event simulation and

agent-based simulation, used to model the effectiveness of caries prevention programs may be useful from

the perspective of planning preventive care dedicated to children in schools.

1 INTRODUCTION

Dental caries has been recognized in the current

century as a social disease that affects more than half

of the world's population (WHO, 2017). It is caused

by teeth demineralization due to a number of factors,

including cariogenic bacteria and sugars

(Featherstone, 2004). Although people of all ages

suffer from it, the severity of the symptoms varies

depending on the type of preventive measures taken,

such as attending educational meetings, dental check-

ups, fluoridation, and sealing of the teeth. The

environment and the views of those around us also

play an important role in caries prevention. A positive

influence of an environmental group may result, for

example, in greater attention to oral hygiene or less

consumption of sugars, or, on the other hand, a

negative influence may exacerbate poor hygiene and

dietary habits. Depending on the environment,

individual attitude may be formed in students.

https://orcid.org/0000-0003-2071-7941

https://orcid.org/0000-0002-6716-9412

Prevention from an early age is crucial and

requires substantially fewer financial resources than

caries treatment. Health policy planning is essential

in the prevention of dental caries disease and is the

focus of much reflection and discussion (Ramos-

Gomez et al., 2020). In planning preventive care, it

may be important to consider the environment for

which care is dedicated. Depending on the region, for

example, students may be more or less aware of

health. They may be more concerned with hygiene or

have better eating habits than in other regions. The

main goal of health care is to ensure the health of the

population by providing access to curative but also

preventive services. Compared to treatment,

prevention is much cheaper. However, to have the

greatest effect in limiting the progression or

occurrence of a disease, it must be introduced enough

early. In the early years of life, parents and caregivers

are responsible for the good oral health and hygiene

habits of children. However, the number of children

with dental caries shows that these individually

340

Hajłasz, M. and Mielczarek, B.

Modelling of the Inﬂuence of the Peer Environment on the Prevention of Caries Development in Schoolchildren using a Hybrid Simulation Approach.

DOI: 10.5220/0011317500003274

In Proceedings of the 12th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2022), pages 340-347

ISBN: 978-989-758-578-4; ISSN: 2184-2841

undertaken measures are insufficient and do not

produce the desired results. Therefore, it is very

important to provide systemic support by conducting

preventive programs in schools.

Simulation methods are playing an increasingly

important role in supporting healthcare-related

decision making (Kisliakovskii et al., 2017).

Simulation methods used in health care can be

classified in different ways; however, the most

common methods are those from four subcategories:

discrete event simulation (DES), agent-based

simulation (ABS), system dynamics (SD), and Monte

Carlo (MC) simulation (Brailsford et al., 2009).

Simulation methods can be used in health care to

support various types of decision. However, each of

them, when used within the same problem, will

potentially produce different results due to their

different characteristics. Therefore, it is becoming

increasingly popular to combine different methods in

one approach. Models based on two or more

simulation approaches such as DES, ABS or SD are

called hybrid simulation. When combining

simulation methods with analytical techniques, this is

called the hybrid systems modelling approach

(Powell and Mustafee, 2014). Applying a hybrid

approach to healthcare can provide decision makers

with a wider and better understanding than is possible

with only one method (Zulkepli and Eldabi, 2015).

Hybrid approaches emerged to take advantage of and

overcome the limitations of individual methods.

When combining DES and ABS, the DES method

covers detailed modelling of the system, including

flows and queues, but omits the possibility of

modelling interactions between units. This feature, in

turn, is an advantage of using ABS, but this method

has the disadvantage of not having a queueing and

flow concept (Abdelghany and Eltawil, 2014).

The aim of this paper is to use a hybrid simulation

to investigate the impact of supportive, neutral, and

non-supportive peer environments on strengthening

or weakening the effectiveness of dental caries

prevention in students of a sample primary school in

southwestern Poland.

2 DATA AND METHODS

2.1 Study Design and Settings

The prevention of dental caries can take many

different forms. From those provided individually in

dental surgeries to group preventive services, usually

held in schools. Few programs in southwest Poland

provide, among other things, additional funding for

services that are not funded by the National Health

Fund. As part of the program: Prevention of dental

caries in students in primary schools in Wroclaw

(Nyczak, 2017), students in selected schools are

provided with preventive actions such as dental

check-up of students with determination of oral

condition and educational, preventive, and

therapeutic needs, stabilization of caries in primary

teeth, sealing of permanent teeth, or treatment of

"punctual" caries in permanent molars. This program

is a multi-year undertaking, implemented in

conjunction with the city's performance budget

planning. Such programs are additional because,

regional governments are responsible for ensuring

that all students have access to preventive care

(Journal of Laws of 2019, 1078). The National Health

Fund finances this care, but the directors of individual

institutions are responsible for providing it.

Education in Poland is divided into several stages,

the first in primary school lasts 9 years: kindergarten

and eighth grades. During education, students are

provided with preventive services: check-ups, sealing

of first molars, fluoridation, and education. It is

assumed that in addition to these services, students

exchange views on oral hygiene and oral health

habits.

Awareness is very important in caries prevention.

Depending on whether the student is aware of the

negative impact of poor eating habits or the good

impact of proper hygiene, he or she may support or

inhibit the development of caries in the oral cavity.

This awareness is influenced by many different

factors, one of which is undoubtedly the closest

environment. In addition to parents, children at school

are surrounded by their classmates.

2.2 Data

Access to actual data describing the phenomenon of

dental caries in schoolchildren in southwestern

Poland is limited. In the present study, we used

aggregated data showing the average number of

primary teeth, permanent teeth, and the value of the

dmft and DMFT indicators (dmft: decayed, missing,

and filled teeth) in children 6,7,10,12 and 15 years of

age (Tables 1 and 2). The dmft indicator is commonly

used in dentistry, the higher the index value, the more

advanced the caries. The symbol dmft is used for

primary teeth and the symbol DMFT for permanent

teeth.

The effectiveness of the preventive services

undertaken was based on reports from the available

literature after consulting with an expert dentist.

Modelling of the Inﬂuence of the Peer Environment on the Prevention of Caries Development in Schoolchildren using a Hybrid Simulation

Approach

341

Table 1: Number of primary and permanent teeth: average

[avg] and standard deviation [sd] in children aged 6, 7, 10,

12, and 15 years. Source: (Olczak-Kowalczyk et al. 2021).

Years

Primary teeth

[av

± sd]

Permanent teeth

[av

± sd]

6 17.64±1.82 4.25±2.59

7 14.83±2.85 8.89±2.87

10 3.88±3.77 19.65±4.03

12 0 25.59±2.94

15 0 27.83±0.79

Table 2: Indicators of dmft and DMFT: average [avg] and

standard deviation [sd] in children aged 6, 7, 10, 12 and 15

years. Source: (Olczak-Kowalczyk et al. 2021).

Years

dmft [avg ± sd] DMFT [avg ± sd]

6 3.65±3.21 0.09±0.47

7 5.42±3.25 0.61±1.12

10 1.62±1.88 1.88±1.63

12 0 3.60±2.74

15 0 5.42±3.69

2.3 Methods

We have constructed a hybrid simulation DES-ABS

model to investigate the impact of the environment on

the effectiveness of dental caries prevention in

students (Figure 1). Both DES and ABS are methods

commonly used in healthcare.

The DES method is a useful method for studying

complex and dynamic systems and is often used to

flow modelling. It has been used in problems related

to more than half of the diseases in the ICD-10

classification (Zhang 2018). For modelling, e.g.,

infectious diseases, the ABS method is particularly

applicable (Tracy et al., 2018). It is a method in which

special attention is paid to the interactions that occur

between the individual components of the system, the

so-called agents. Therefore, the combination of these

two methods enables the flow modelling and taking

into account the interactions that occur during the

simulation between the different agents (Abdelghany

et al., 2016).

The DES method was used to model the

educational process in primary school along with

preventive services provided such as dental check-

ups, sealing of first molars, fluoridation, and

education. An ABS method was used to model

interactions between agents, who are students. The

combination of these two methods allowed verifying

the effect that contact with peers can have on

increasing or decreasing the effectiveness of

preventive services.

Figure 1: Hybrid simulation: overview of the DES-ABS model.

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The DES part is responsible for simulating the

growing process of children over the course of their

primary schooling. Each student starts school with

values for four basic attributes: primary and

permanent teeth, dmft, and DMFT taken from real

data. Then, preventive services are provided during

their nine-year education. Indicators are updated once

a year. Graduation students have a given number of

permanent teeth and a DMFT indicator value.

The time and effectiveness of the measures taken

influence the update of the indicators. Part of ABS is

responsible for tracking students' attitudes toward oral

health care. Each student, through contact with other

students, can change his or her attitude towards taking

care of health. Students change their closest

environment at school by changing their classmates

with whom they share their opinions about oral health.

After any change in the environment, their individual

attitude (IA) towards oral hygiene care, dietary habits,

or overall attitude toward oral health may change.

Depending on whether immediate peers have a

negative, neutral, or positive IA, the effectiveness of

preventive services may be decreased or increased.

3 SIMULATION MODEL

3.1 Overall Algorithm

The hybrid model was built in Arena by Rockwell

Automation. Ten replications were conducted; one

replication covered 6570 days, or 18 years. A warm-

up period of half that time was assumed so that the

school would be filled with students before statistics

collection began. A classroom of 20 students was

observed, and the effectiveness of preventive services

was tracked over time without and after taking into

account social influence.

The DES model with verification and validation

is presented in detail in Hajłasz and Mielczarek

(2022). The effectiveness of preventive services was

developed with a dental expert based on reports in the

literature. Effectiveness is understood as the

percentage that accounts for the reduction in caries

growth that would have occurred if these services had

not been provided.

The ABS model assumes that each student can be

assigned one of three attitudes toward oral hygiene:

IA negative (-1), IA neutral (0) and IA positive (+1).

At the beginning of the simulation, each student is

assigned an IA value based on his or her oral health.

To simulate the interactions between the students, a

two-dimensional grid was constructed, which is a

typical cellular automaton. Each field represents a

space that can be occupied by a student. Students

change their surroundings and, by extension, their

neighbors. Figure 2 shows the initial example setup

(0) of the students along with an example change (1).

Each shaded grid corresponds to one student with an

ID number of 1 to 20. Each time, each student

randomly shifts to one of eight adjacent grid squares.

Then the IA of neighboring students are checked, and

a given student can change its IA.

Figure 2: The example of the students' closest environment

in the initial state and one example change.

Each student exchanges his or her views with

different classmates. The attitudes of classmates can

change a given student's attitude, so his or her IA can

change depending on three conditions. If the

summative IA of the closest surrounding students is

less than a given student's IA, then there is a 50%

chance that a given student, if he or she has a positive

or neutral IA, will change it to a negative IA. If, on

the other hand, the summative IA of the clostest

surrounding students is greater than a given student's

IA, then there is a 50% chance that a given student, if

they have a negative or neutral IA, will change it to

positive. If the summative impact of the closest

surrounding students is the same as a given student's

IA then nothing changes. There is also no chance of

changing the IA from negative or positive to neutral.

Modelling of the Inﬂuence of the Peer Environment on the Prevention of Caries Development in Schoolchildren using a Hybrid Simulation

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343

The closest environment is understood as the students

occupying cells immediately adjacent to a given

student cell in the grid.

The IA of students is read at the time of updating

the dmft and DMFT indicators in the DES model, i.e.,

at the end of the school year. Depending on whether

a student's IA is negative, neutral, or positive, this

changes the baseline effectiveness value of the

preventive services undertaken.

The main output measure is the average number of

pupils having a certain sum of dmft and DMFT at the

end of each school year. Depending on this sum, each

student is classified into one of three dental caries

states (DCS): good, moderate, or bad (Table 3). Over

time, the values of the dmft and DMFT indicators

change, which may cause a change in the DCS class.

These classes were defined and named by the authors.

Table 3: Three states of dental caries state (DCS) depending

on the sum of dmft and DMFT in each pupil.

DCS dmf

+ DMFT

Goo

Moderate 1-3

4 and more

3.2 Simulation Experiments

Three simulation experiments were conducted (Table

4). In the first experiment, it was assumed that students

are provided with regular fluoridation, dental check-

ups, sealing of first molars, and education, and the

effectiveness of the services is expressed as a

percentage and generated from triangular distributions.

Table 4: Plan of the experiments.

Scenario Effectiveness of caries prevention

1 The same applies to each pupil

2 Variations b

IA updated annuall

3 Variations b

IA updated twice a

The parameters of the distributions in the first

experiment are independent of the IA value of a given

student, that is, they take values corresponding to

neutral IA (Table 5).

In the second and third experiments, IA is affected

by contact with closest peers. In the second

experiment, students change their environment once

a year, while in the third experiment, they change

their environment twice a year. Initial IA values are

generated depending on the initial value of DCS

indices, i.e., how many primary and permanent teeth

with dental caries a given student has. If he or she has

all healthy teeth, then the initial IA is +1, if he or she

has 0 to 3 teeth with caries, then the IA is 0, if he or she

has more than 3 teeth with caries, then the IA is-1.

Table 5: Effectiveness of preventive services depending on

a student IA: most frequent value, and range of triangular

distribution.

IA Primar

teeth (%) Permanent teeth (%)

-1

23 (17,27)

77 (71,81)

0 26 (20,30) 85 (79,90)

1 29 (23,33) 93 (87,97)

3.3 Simulation Results

The DES model was able to track changes in the

average number of students with a given DCS

indicator. On the contrary, the ABS model provided

information to the DES model about how the level of

effectiveness of preventive services varied by student

IA. Figures 3 and 4 show how the average number of

students with a given IA evolved depending on

whether the students changed their closest

environment once a year (scenario 2), or twice a year

(scenario 3).

Figure 3: Average number of students with one of the three

IAs (-1,0,1) at each age for which the effectiveness of

preventive services was updated, assuming that students

change their closest environment once a year.

Figure 4: Average number of students with one of the three

IAs (-1,0,1) at each age for which the effectiveness of

preventive services was updated, assuming that students

change their closest environment twice a year.

7 8 9 10 11 12 13 14

Average

number of students

Age

-1 0 1

7 8 9 1011121314

Average

number of students

Age

-1 0 1

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Figure 5: Comparison of the average number of the same group of 20 students with a given DCS class in all experiments

conducted; results of 10 replications.

Table 6: Average number of students with one of the three DCS classes in each of the three experiments. Average of 10

replications for 20 students.

DCS Scenario 6 7 8 9 10 11 12 13 14

Good

1 6.4 5.2 4.4 6.1 6.4 6.7 6.7 4.6 3.9

2 5.8 5.5 4.5 7 8.5 8.8 8.6 6.7 5.5

3 6.3 3.9 4.4 6.1 8.8 9.8 8.3 6.5 5.2

Moderate

1 6.4 5.3 8.2 8.8 9.8 12 13 15 16

2 5.7 4.5 6.9 7.3 9.2 10.6 11.4 13.3 14.5

3 5.9 6.7 6.8 7.7 9.4 9.9 11.7 13.5 14.8

Bad

1 7.2 9.5 7.4 5.1 3.8 1.4 0 0 0

2 8.5 10 8.6 5.7 2.3 0.6 0 0 0

3 7.8 9.4 8.8 6.2 1.8 0.3 0 0 0

In the first scenario, the average group of children

with good and moderate DCS at graduation was 3.9

and 16 students, respectively (Figure 5). In the

experiments that included IA, whether the students

changed their environment twice a year or once, the

results were similar for these experiments. With good

DCS they graduated an average of 5.5, with moderate

DCS 14.5 in the second experiment. In the third, 5.2

and 14.8, respectively (Table 6).

Students may change their IA several times during

their primary education, which impacts the

effectiveness of services, which translates into the

number of students with a given DCS.

4 DISCUSSION

Caries disease is a disease that is the result of many

factors. It is also a disease that is relatively easy to

prevent. This is confirmed by the literature reports

and conducted studies. Preventive services regularly

provided to schoolchildren can significantly reduce

Modelling of the Inﬂuence of the Peer Environment on the Prevention of Caries Development in Schoolchildren using a Hybrid Simulation

Approach

345

the problem of caries. The effectiveness of preventive

measures, in addition to the effectiveness of medical

procedures, is influenced by individual attitudes and

behaviour of students. The present study considers

individual attitude of students, which is randomly

shaped by a student's interactions with his or her

closest peers within a single classroom.

If the majority of students have the IA equal to 1,

which corresponds to positive attitude, there is a

much greater chance that this group will convince

children with the IA equal to 0 or -1 (neutral and

negative) that hygiene and healthy habits are worth it,

which in turn may results in reduced caries.

If, on the other hand, the majority of children had the

IA equal to -1, this could lead to a deterioration in the

health of the students in the class. much greater

chance that this group will convince children with the

IA equal to 0 or -1 (neutral and negative) that hygiene

and healthy habits are worth it, which in turn may

results in reduced caries. If, on the other hand, the

majority of children had the IA equal to -1, this could

lead to a deterioration in the health of the students in

the class.

The hybrid simulation that combines DES and

ABS approaches allows testing many different

scenarios of the effectiveness of preventive services

together with the interactions that occur between

students at the school. The DES simulation alone

cannot verify this impact, and it is believed that in the

context of dental caries prevention, awareness of the

importance of good hygiene and diet is important and

may or may not support the effectiveness of other

measures such as fluoridation, sealants, check-ups, or

education.

5 CONCLUSIONS

This study identified the usefulness of hybrid

simulation to investigate the impact of supportive,

neutral, and nonsupportive environments on

strengthening or weakening the effectiveness of

dental caries prevention in students of a sample

primary school in southwestern Poland.

The main strength of the suggested approach lies

in the ability to comprehensively follow the

development of dental caries in students in different

scenarios, taking into account not only the

effectiveness of services, but also individual social

interactions. The primary limitation of the present

study is the limited access to detailed source data.

Therefore, further research primarily is planned to

acquire detailed source data. Additionally, school

surveys are planned to verify the IA in students

according to the region of residence of the students,

among others. It is also planned to conduct

experiments taking into account more classers or

schools and the students' region of residence or other

demographic factors that may influence the formation

of individual student attitudes toward oral hygiene,

broadly defined.

ACKNOWLEDGEMENTS

This project is financed by grants from the National

Science Centre, Poland based on decisions:

2021/41/N/HS4/03282 “Hybrid modelling of the

demand for specialist dental care in the field of dental

caries prevention in children using computer

simulation” and 2015/17/B/HS4/00306 “Simulation

modelling of the demand for healthcare services”.

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