Using complex System Dynamic models;
an example concerning the Dutch dental health care system
E.M. Bronkhorst, M.Sc; T. Wiersma, M.Sc; GJ. Truin, PhD., D.D.S.
Department of Cariology and Endodontology
Research Program "Dental Health Care and Epidemiology”
TRIKON: Institute for Dental Clinical Research
University of Nijmegen
P.O.Box 9101
NL-6500 HB Nijmegen
The Netherlands
ABSTRACT
Recently a System Dynamic simulation model of supply and demand of the dental health care
system in The Netherlands has been developed. This model includes major demographical,
pathological, psychological, sociological and economical processes comprising the demand side.
The supply side covers the availability of dentists, dental hygienists and factors which deter-
mine their productivity.
The main purpose of the model is to create an instrument for analysing the Dutch dental health
care system. A relatively simple model with e.g. 20 state variables just describing the main con-
cepts of this system was not considered to be sufficient. Therefore, starting from a simple
model, during the past decade a far more complex model has been developed. It contains for
instance 440 state variables, This model has already proven to be very satisfactory with regard
to its descriptive qualities. However, the necessity for working with complex models has also
negative side-effects. Apart from the great efforts needed constructing, validating and analysing
the model, it is well known that the more complex the model, the more difficult to communi-
cate about its results and properties, with people for whom the model might be useful. This is
even more so if it concerns people from outside the academic world (in this case for instance
the dental profession or policy makers).
In this paper attention will be focussed firstly on a short introduction concerning the model
and its structure. Secondly, our experiences with the model will be used as an example of our
ideas about how to construct sophisticated models with a high descriptive quality, while at the
same time making them at least acceptable for those who might use its results, but were not di-
rectly involved in the construction of it.
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1 INTRODUCTION
A major problem for people working in the field of System Dynamic modelling is the discrep-
ancy between the potential of System Dynamic techniques as perceived both by System Dy-
namic experts and their clients, and the actual impact of System Dynamic modelling. Especially
evaluations of projects concerned with System Dynamic modelling in the public sector have
often brought to light that the actual impact on the people who have the power to use the
model’s results has been minimal. A bottle-neck often encountered is the transfer of experi-
ences and knowledge of the model constructors to the users of the model’s results. Two possi-
ble solutions for this problem are the demand for small models concerning restricted problems
and involvement of the intended users of the model’s results in every phase of its construction
(Meadows and Robinson, 1985).
In this paper we will discuss a project in which a model of the Dutch dental health care system
was developed. For reasons discussed later in this paper both of the two options suggested to
facilitate the transfer of knowledge were not feasible. We certainly do not pretend that we can
give a methodology of eliminating the problems occurring in communicating about the results
of this type of projects. This paper can be considered, however, to be a case study concerning
some practical aspects of making complex models easier to understand.
2 THE MODEL AND ITS HISTORY
During the past decades the imbalance between demand and supply of dental health care in The
Netherlands has been a matter of serious concern, In attempting to tune supply and demand,
policy-makers have to deal with a complex socio-political system and as a consequence of this,
with a dynamic, non-equilibrium system (Forrester 1969; Mesarovic, 1970; Klabbers et al.,
1980). It has become increasingly clear that both systems-approach and computer simulation
offer favourable perspectives for a more adequate integration of policy-options in complex so-
cial systems.
For the sake of surveying and investigating the structure and behaviour of the dental health
care system more systematically in 1979 a research project has been initiated at the dental
school of the University of Nijmegen on System Dynamic computer-simulation models of the
dental health care in The Netherlands. In the past ten years three System Dynamic models have
been developed. The model which is subject of this case study is the third model. Since its
structure and characteristics are rooted in the two predecessors we will not only give a descrip-
tion of this third model but also briefly introduce the first two models.
Firstly, a relatively global model was developed. The relative simplicity had some disadvan-
tages. For instance, no difference was made between age-groups and only one “treatment” was
considered, This model has been embedded in an interactive computer-simulation game
(Klabbers et al., 1980). In this game three groups of actors were considered: government,
parliament and the dental profession. Each group only had access to partial information and
different policy measures. The experiences during the game-sessions were twofold. Firstly,
players were enthusiastic and expressed to have gained valuable insight in the complexity of the
issue. Secondly, especially dentists felt the need to look into the problem area in much more
detail, focussing on age-groups, pathology etc.
System Dynamics ‘90 157
As a result of this experience a model more detailed in its description of the dental health care
system was developed and implemented on a mainframe computer (Truin, 1982). This model
had a level of detail specialists in the field of planning the Dutch dental health care system con-
sidered minimal to give an adequate description of the dental health care system. The popula-
tion for instance was differentiated by age, insurance status and dental attendance behaviour.
The model consisted of two submodels concerning pathology, a submodel concerning the den-
tal attendance behaviour, a submodel covering the supply-side and a submodel covering the 12
most important treatments. The model was able to reproduce fairly well the behaviour of the
Dutch dental health care system as observed for the period 1970-1984, and it has been used to
perform scenario-analyses concerning dental health care during several years. However, due to
the implementation on a mainframe which made the model quite difficult to handle and due to
its complexity, it was very difficult to communicate about the results of the model. Mainly for
this reasons it was decided to develop a third model. Roughly speaking this model was intend-
ed to be at least as good as the second model with respect to its descriptive qualities, while at
the same time eliminating its drawbacks.
3 OVERVIEW OF THE MODEL
3.1 Global properties of the model
The model is a deterministic discrete time model with time steps of one year. It contains about
440 state variables and the number of parameters is over 4000. The model and its supporting
software is implemented in Pascal on a Macintosh IIcx computer. Amongst the supporting
software are facilities for quickly reviewing the results of a run, and software for changing pa-
rameters by filling out spreadsheets. Total runtime for a 40-year run using all submodels is
about 5 minutes.
3.2 Model structure
The entire model can be seen as three linked models. The first part being a population model,
the second part consisting of submodels modeling the demand side of the dental health care
system and the third part describing the supply side.
The population model is off-line and acts as a driving function of the demand model. It gener-
ates data of a population consisting of seven age groups. Each of these age groups is subdivided
into two or more groups with a different socio-economical background. These groups for in-
stance may represent people with different socio-economical status (SES) or may reflect differ-
ences between people taking part in different insurance-programs. In the implementation dis-
cussed here the subdivision into socio-economical groups is based on the criterion “insurance”:
the first socio-economical group consists of people participating in a public insurance system
called the Sickfund comprising about 70% of the population, the second of people having a pri-
vate insurance for their health care expenditure.
The Demand model includes four submodels: Visit, Caries, Periodontal Diseases (i.e. the PD-
model is concerned with diseases of the tissues supporting the teeth: bone tissues and gums)
and Treatment. Each socio-economical group in the demand model in its turn is subdivided
into three groups: people visiting a dentist regularly, people visiting a dentist irregularly and
158 System Dynamics '90
people without a natural dentition (edentulous). The population structure thus obtained is the
backbone of the model. Notwithstanding the links between the different cells of the population
(induced for instance by demographic processes or changes in dental attendance behaviour) the
Demand model contains a complete and self-contained submodel of each cell. As a result of
this for each cell a set of state-variables (e.g. average number of decayed teeth per person, or
percentage of people suffering from calculus) and a set of parameters (ranging from sugar-con-
sumption to price-sensitivity for dental treatments considered) is provided. An impression of
the model structure is given in figure 1. All cells have the same internal structure. For obvious
reasons the cells containing edentulous people have a much simpler structure.
Sickfund Private Insurance
Regular Irregular Edentulous Regular Irregular Edentulous
0-5
6-12
dentist
Decayed Filled
13-18 teeth =a teeth
hygiene
dentist dentist
19-29
Extracted
teeth
30-44
oral
hygiene
Gingivitis Pockets
as ee dentist
65+ with 4
[Calculus >
\
Figure 1: Structure of the model at population level
System Dynamics '90 159
In the Supply model it is calculated how many full-time equivalents (fte) are available for tasks
related to the treatment of patients. This is done separately for dentists and dental hygienists.
The Supply model and the Demand model are dynamically linked. This is done mainly by two
variables. The submodel Treatment uses the number of fte available which is calculated in the
Supply model and the Supply model uses the workload for dentists and dental hygienists
which is calculated in the Treatment model. In the figure below an overview of the submodels
building the overall model and the major interactions between these submodels is given.
Population
differen-
tiated by
insurance
_| Periodontal
diseases Demand
1
1
1
il
Supply
Changes in ' Information Changes
population \ due to
structure 1 treatments
Figure 2. Submodels building the overall model
160 System Dynamics '90
4 HOW WE MADE THE MODEL MORE ACCESSIBLE
Before we discuss some decisions we have made to make the results of the model more acces-
sible, we firstly want to clearly distinguish between two very different types of the use of re-
sults of System Dynamic models: these can be referred to as the “figure”-level and the
“insight”-level. By the “figure”-level we want to express the direct use of results of a model,
often given.in figures or graphs. In this type of use the reference run is interpreted as a predic-
tion of the future behaviour of a system, results of scenarios are considered to give an accurate
assessment of the impact of certain changes in policy decisions or values of parameters, When
using System Dynamic models in this way the model often is viewed as a black box. Looking at
our experiences in the past the question whether results of System Dynamic models are used
on the “figure*-level is determined mainly by two factors. The first factor is the authority of
the constructors of a model and/or the institute they are working for. The second factor con-
sists of the results themselves. If they suit a certain group of possible users they will certainly
use them, if not the results will not be used. The case study in this paper is not about possibili-
ties for making the use of model results on the “figure”-level more efficient. This has two rea-
sons. Firstly, the two factors determining to what extend model results will be used on a
“figure”-level can not easily be influenced. Secondly, this is not the level of use the project con-
cerning the Dutch dental health care system was aiming for.
This project aimed for the construction of a System Dynamic model which could be used on
the “insight”-level. On this level the model is used to identify processes responsible for the dy-
namic behaviour of the main variables in a system, integration of knowledge from different sci-
entific fields concerning the system into one coherent framework, ruling out contradictory
policy options, separating attainable and unattainable policy goals etc. The discussion of the
decisions made to make the model more accessible is entirely focussed on the use of the model
on the “insight”-level.
In our discussion we want to make a distinction between two groups of ideas concerning the
accessibility of our model. The first group consists of ideas more or less directly related to the
contacts with users of the model’s results, the second group are the ideas related to the struc-
ture of the model.
41 Considerations with regard to the contacts with users of the model
In the period that we were about to finish the construction of the model with respect to the
model structure and were able to start the validation, we were asked by the Department of
Public Health to establish a scenario project in the field of dental health care. Object of this
scenario project was to bring together a group of representatives of the most important groups
active in the field of dental health care (the scenario committee). General aim of the project
proposed to us was to gain insight in the developments of the state of oral health of (some parts
of) the Dutch population in the next 25 years, and to analyse the effects and side-effects of
policy options being considered and changes in the dental health care system, such as proposed
changes in the structure of the insurance system. The scenario committee consisted of dentists,
dental hygienists and economists representing the universities, the Dutch Dental Association,
the Dutch association of dental hygienists, public and private insurers and the Sickfund board.
System Dynamics '90 161
From this project and our experiences with these users, we compiled five basic notions dis-
cussed in sections 4.1 and 4.2, which we think might be useful for others working in projects
with complex System Dynamic models.
4.1.1 Reconstruct models in cooperation with its users
Although the model’s structure was more or less completed, we decided to use the opportunity
offered by this project to establish a “quasi” participatory model construction. So we discussed
thoroughly the content of each submodel, giving the scenario committee the opportunity to
suggest changes they felt necessary to answers the questions they had in mind. This approach
demanded a large time investment of the research group which resulted only in minor changes
in the original model. But the whole process has been very fruitful with regard to its intended
side-effect: making an important group of users of the model acquainted with the model and
giving them the feeling that this isn’t just a model but, at least partially, their model.
For System Dynamic modeling involving very complicated models due to the mere time span
of the model construction it can be very difficult to create a participation of the intended users
of the model and its constructors. In these situations we think it might turn out to be an effi-
cient investment of time to reconstruct the entire model with groups of users, thus strongly en-
larging the chance that the model will be used on the “insight”-level.
4.1.2 Keep discussion about structure and validation wide apart
During the meetings with the scenario committee it turned out that whenever structural aspects
and validation were discussed at the same time, it was impossible to make any progress. One
might say that understanding a model only has to do with being familiar with its structure and
is completely independent of its validation. Validation is most important for giving people
confidence in the results of a model. So when trying to let people understand a model don’t
talk about validation. As soon as people understand and accept the structure of a model, dis-
cussing questions related to validation will be less complicated.
4.1.3 Donot bother someone with all details
A very important factor determining the behaviour of our model is the population model. For
instance, the oral situation of the 55-years old in 10 years depends on a large set of variables,
the most important one being the oral situation of the 45-years old now. So in explaining the
model we were tempted to spend a lot of time talking about the population model and its inter-
actions with the pathology models. This turned out to be a waist of time. The intuitive ideas
people had about the population model and its interaction with the rest of the model come
very close to the actual implementation and in that case not much is gained by a discussion of
the ins and outs of the population model.
4.2 Considerations with regard to the model structure
4.2.1 Let the model consist of submodels which are as independent as possible
The reason for this is relatively simple. A strength of System Dynamic models is the possibility
to incorporate explicitly dynamic relations between various variables. In the mental models
162 System Dynamics '90
people use this type of relations is often absent. As a consequence discussions about the con-
tent of a submodel will become more difficult if it can not be separated from dynamic feedback
relations between variables in more or less “remote” parts of the model.
In our model an example can be found when looking at the Supply model. We have chosen the
working potential, for tasks related to treatments, of dentists and dental hygienists as the only
output of the Supply model and its only input from the Treatment model is the utilization level
of dental services. By this choice discussion of the Supply model can focus entirely on its in-
tended themes such as the age structure of the dentist population, fractions of people leaving
their profession, number of students in education etc. If only a small part of the processes
governing the management of practices by dental practitioners were part of this submodel,
communications about this submodel are very likely to be “contaminated” by the need to ad-
dress questions concerning treatment strategies, relations between changing pathology and the
need for dental care etc.
42.2 Make relations as flexible as possible
On the previous page we discussed the fact that talking about the structure of a model and
about its validation should be kept wide apart. This will only be possible if relations in the
model are implemented flexibly. Looking at our model for instance, the chance that sound
teeth will become decayed will depend on the use of sugar and the fluoride intake. So in the
model functional relationships between both the use of sugar and the fluoride intake and the
chance of becoming decayed had to be incorporated. To allow for a very wide set of possible
relations, the model contains not only two sets of six parameters defining these relations
separately for each cell of the population, but also the possibility to choose from a variety of
interactions by simply changing parameter values. The flexibility we aim for can also be
achieved using other constructions, but anyhow, maximising the opportunities to tune a model
by picking the right parameter values is important.
This flexibility has also other advantages. The construction of complex models is very expen-
sive and takes lots of time. By making the model flexible the time span in which the model can
be used without the necessity for major changes can be enlarged. Besides this, a flexible model
can more easily be transferred to other similar situations. In our research project we intend to
start a project where our model will be adapted to the British situation. First impressions are
that large parts of the model can be used after only minor adjustments. If we would try to
transfer the predecessor of our last model, this would take a far larger amount of time, although
its content is very comparable; it just lacks the necessary level of flexibility.
5 DISCUSSION
Communications about System Dynamic models are most effective if the models are relatively
simple and have a restricted problem as its subject. Participation of the intended users of a
model in every phase of its construction can also be recommended to maximise the impact of
System Dynamic models. Unfortunately, in certain cases the construction of a complex model
can turn out to be a necessary condition for its results to be accepted and for practical reasons
full participation can be impossible. In this paper a model of the Dutch dental health care sys-
System Dynamics '90 163
tem is introduced which is presented as a case study about communicating about complex
models. A number of our ideas about how we tried to reduce problems in transferring the
model’s results are discussed. A project in which these ideas are brought into practice is now
halfway its two-year period. Though maybe a little premature, our experiences with this pro-
ject indicate that the approach of participatory model reconstruction turns out to be fruitful
and essential for the success of the project.
We have established a situation which takes position between two modus operandi. The first
modus is to build a simple model together with the people who should use it. As we discovered
with our first model, this is useful for those who take part in the project, but the resulting
model was too superficial to have an intrinsic value. The second modus is to construct a com-
plex, highly detailed model without direct cooperation of possible users outside the academic
world, This can result in a model which has a high intrinsic value, but which for possible users
will remain a black box which makes its use on an “insight”-level hardly possible.
Our approach now, which is a compromise between these more extreme approaches, already
resulted in a model which has a relatively high level of detail and has been constructed in co-
operation with a scenario committee consisting of representatives of the organisations which
might use it. The second year of our project will be used for scenario analysis and then the
effectiveness of the cooperation will come to an important test. How will the directly involved
representatives react on results which conflict with their interests? As we see it now, our
approach has involved enough participation of the scenario committee to grow above the
“figure”-level of use and make them think about the how and why of the results of this System
Dynamic model.
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Mesarovic, M.D.; Macko D. and Takahara, Y. 1970. Theory of hierarchical, multilevel systems.
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