STOCHASTIC TEST ON THE MODEL FOR DENTAL DISEASES
Toshiro Shimada, Meiji University, Tokyo, Japan
Takahiro Kojima,Senshuu University,Kanagawa Prefecture,Japan
Abstract
We reported the model for dental diseases at the 1987
and 1992 International System Dynamics Conference.
The model contained 5 sectors; demography, cavities,
pyorrhea, baby teeth, and technology. The demographic sector
covered populations of 5 three-year age groups under 14
years of age and 13 five-year age groups above 15 years
of age. The cavities sector and pyorrhea sector were com-
posed of populations of five-year age groups, on the other
hand,‘ the baby teeth sector used populations of three-year
age groups. By the technology sector we treated innovation
effect on the model.
From the total number of defective teeth, total dental
costs in Japan were calculated annually from. 1963 and pro-
jected to 2025.
We added to this model random number variables, mainly
in the demographic sector and we are testing stochastic
changes on behaviors of various: variables. of the model.
Simulation runs with random birth rate changes show
how their results are changed from the basic run.
1. MODEL FOR DENTAL DISEASES
1.1 Parts composing the model
This model consists of 5 sectors: demography, dental
caries, pyorrhea, baby teeth, and technology. In each sector
we deal with all of Japan. Relations among sectors are
shown in Fig.1.
1.2 Demographic Sector
The demographic sector covers populations of 5 three-
year age classes under 14 years of age and 13 five-year
age classes above 15 years of age. The former are the
classes 0-2, 3-5, 6-8, 9-11 and 12-14 years of age, and
the latter are the classes of 15-19, 20-24, , 70-74 and
75- years of age. The population of each age class depends
on the rates of birth and death. The first age class 20
begins with births and ends where a new age class begins
or, through deaths within the age class. Our other age
classes 23, 26, , 275 follow this same pattern.
486 SYSTEM DYNAMICS '93
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Fig.1 Relation among Sectors
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Fig.2 Flow Diagram for Demographic Sector
488 SYSTEM DYNAMICS '93
1, 3 Dental Caries Sector
The Dental Caries Sector has 13 subsectors corresponding to
13 five-year classes of the population sector.
Dental caries are classified as follows:
Healthy teeth : Carious symptoms and dental care are not recognized.
CO : Similar to healthy teeth, but there is no agreement as to whether
teeth are decayed or not.
C1 : Small surface cavities which may be easily filled and treated.
C2: Cavities are worse than in Cl, but health teeth may be
restored by fillings being done without pulpectomy.
C3: Cavities are worse than in C2, after pulpectomy. In some “cases
decayed teeth are only filled, but generally metal crowns may
be used. In the case of front teeth complete care of bridges may
be necessary. eS
C4; Carious symptoms are ‘serious enough that decayed teeth must be
extracted and a denture may be necessary.
The number of C1 teeth is first computed. Then C2,C3,C4, filled
teeth, crowns and bridges, missing teeth and dentures are
successively computed as seen in Fig.3. :
Data for this sector have all ‘been collected by the Japan
Dental Association. :
Dentures
\ Va Met
Fillings
eee ceeennn
Fig.3 Relation among Diseases
SYSTEM DYNAMICS '93 489
2. THE EFFECT OF THE RANDOM NUMBER FUNCTIONS ON VARIABLES
OF DEMOGRAPHIC SECTOR
Random birth rate changes were added to the basic
model,
The mean was set equal to 0 and the standard deviation
for each class was derived from the historical data by
the least square method.
Fig.4 and Fig.5 show populations for the basic run
and the run for random birth rates.
Fig.6 and. Fig.7. show birth rates of the basic run
and the run for random birth rates. Of course, the latter
fluctuates severely. :
Populations seen in Fig.5 are different from those
in Fig.4. However, the long term trend seems’ not to be
so much influenced, in spite of- the remarkable changes
of birth rates.
Random changes used in these runs are a sequence of
random numbers generated in DYNAMO, and ;by other sequences
with the same mean and the same standard deviation we
obtained other runs, which are, of course, different from
each other, but populations. for each run show not so much
difference.
3. CONCLUSION
We have attempted to formulate a System Dynamics: model
for dental diseases which have five sectors of demography,
dental caries, pyorrhea, baby teeth and technology.
We added to this model random birth rate changes.The
simulation results show that the long term trend seems
not to be so much influenced, in spite of the remarkable
changes of birth rates.
REFERENCES
1.Shimada Toshiro,Kenji -Fukushima,Kinya Machida and Akira
Uchino,"A Simulation Model for Dental Diseases", Procee-
dings of the 1987 International Conference of the System
Dynamics Society,pp.476-481,1987.
2.Shimada Toshiro,Hirokazu Mizushima,Takahiro Kojima and
Koichiro . Okumura,"Innovation.. Effect on the Model for
Dental Diseases", Proceedings of the 1992 International
Conference of the System Dynamics Society,pp.685-694,1992.
490 SYSTEM DYNAMICS '93
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494 SYSTEM DYNAMICS '93
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