Making System Dynamics Cool II: New Hot
Teaching and Testing Cases of Increasing Complexity
Erik Pruyt*
July 22, 20104
Abstract
This follow-up paper presents several actual cases for testing and teaching System Dy-
namics. The cases were April 2009 and January 2010 for the Introductory
System Dynamics cour: sity of Technology in the Netherlands. They can be
used for teaching and testing introductory System Dynamics courses at university level as well
as for self study. The cases included here range from easy/short to difficult/long.
Keywords: System Dynamics Education, Actuality, Hot Teaching and Testing Cases,
Pneumonic Plague, Mexican Flu, DSB Bank Run, Scarcity of Minerals/Metals
1 Introduction
The aim of this paper is —just like the aim of the first paper on Hot Teaching/Testing Cases
to share actual teaching/testing cases. The rationale behind this goal is two-fold:
I believe that (higher) education determines to a large extent the quality of (the next genera-
tion of) professional System Dynamics modellers, and hence, the field of System Dynamics (SD).
Second, I believe that sharing (innovative and/or proven) educational practices, and exchanging
teaching/testing cases may lead to the further development of SD education.
Two of the SD courses taught at the Faculty of Faculty of Technology, Policy and Management
of Delft University of Technology are mandatory for BSc and MSc students: an introductory SD
course and a SD project course (see for more information on the SD curriculum
at Delft University of Technology). The introductory SD course is in fact a prerequisite for the
SD project course.
Until 2006, small/didactic and technical/mathematical SD exercises were used during vol-
untary computer labs of the introductory SD course to familiarise students with SD modelling.
Computer-aided modelling and simulation were not tested during predominantly multiple choice
exams. However, the case of the SD project was —and still is~ rather large and difficult, and re-
quires at least intermediate SD modelling skill
and irrelevant information, uncertainties and contradictions, information and indications needed
to specify the SD simulation model (see (Meijer, Pruyt, and Slinger 2010) and (Slinger, Kwakkel,|
{and_van der Niet 2008)). At that time, the transition from small/didac ses to the big
project case went —at least for many students~ anything but smoothly. The gap between the
exercises dealt with during the non-mandatory computer labs of the introductory SD course and
it has broad, fuzzy boundaries, contains relevant
exer
“Corresponding author: Erik Pruyt, Delft University of Technology, Faculty of Technology, Policy and Manage-
ment, Policy Analysis Section; P.O. Box 5015, 2600 GA Delft, The Netherlands nail:
+Published as: Pruyt, E. 2010. Making System Dynamics Cool II: New Hot Teaching and Testing Cases of
Increasing Complexity Proceedings of the 18th International Conference of the System Dynamics Society, July
25-29, Seoul, Korea. (Available online at {www.systemdynamics . org) )
1The introduction and conclusions of this paper are to a large extent similar to the corresponding sections of
Pruyt 2009)
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Cases
the large case study of the SD project course w
bridged without serious difficulti
simply too big for part of the students to be
several changes to the introductory SD Course were made in 2007-2008 (see
2009)) in order to quickly ramp up practical SD modelling skills of all students. One
of these changes was the introduction of compute d testing of practical modelling skills as
part of their exams — which seems to be a good incentive for students to invest in acquiring the
ry applied SD modelling skills during the introductory SD course. Another change was the
introduction of more difficult exercises and cases, at first purely didactic cases, and later also ‘hot’
real-world (which are almost automatically more difficult).
Today, all exercises and cases used in weeks 3, 4, 5, 6, 7 (out of 7) of the introductory SD
as well as all exam models~ deal with relevant and current real-world issues of increasing
s instead of just bigger and more difficult
cases allow to illustrate the relevance of SD modelling for real-world show students what
exploratory SD models of real-world issues may look like, spur students on to look
at current issues from a SD perspective, get students to connect news stories to potential SD
models, and to enthuse students for applying SD modelling to real-world
cases
course
complexity. ‘Hot’ real-world testing/teaching cas
and one SD modelling case. The modelling case consists of one to two pages of detailed cas
description and some guiding questions (see the appendix for examples). Case descriptions for the
introductory SD course are usually very detailed, specifying almost all variables (in italics) and
relationships (mostly in plain language). Case descriptions are followed by about ten questions,
guiding students step by step through all modelling phases, asking students to generate and in-
terpret simulation runs, design and test (closed-loop) policies and to derive and formulate policy
recommendations.
Anecdotic evidence suggests indeed that students find it inspiring and motivating to work on
relevant issues, even if they are more difficult. During the computer labs, many (motivated) stu-
dents persevere for hours at modelling these real-world cases until they finally obtain simulation
results similar to the ones available on {http://forio.com/simulate/e .pruyt/| and/or black-
board, more so than for purely didactic cases. Students also comment after taking the exam that
the case was ‘difficult but very interesting’. An additional advantage related to the use of hot
cases is that students become more aware of the applicability of SD to real-world issues. More
(and more) BSc thesis student nowadays choose an appropriate topic for a SD the
first supervisory meeting. In fact, we are currently witnessing a boom in SD BSc the
in 2012-2013 lead to a boom in SD MSc theses.
Moreover, these SD conference paper on hot teaching/testing cases have lead to many posi-
tive (re)actions from SD scholars and future SD practitioners2, from former students interested in
maintaining their modelling skills, and from clients/profe: ing to develop
in-house SD modelling skills.
before their
This may
ional organisations des
Each year, many testing cases need to be developed for the introductory SD course since:
© about 150-230 students take the introductory SD courses at Delft University of Technology
each year;
« they can take the exam twice a year (and the 55% passing rate is relatively low but —given
One reviewer wrote that:
‘your focus on ‘hot’ topics [and other aspects of the SD curriculum] is a great learning approach. As a
former student of [the world-famous SD professor], I learned a great deal, but it was largely abstract
I therefore have kept modeling and even the use of SD as a small part of my professional practice
rather than front and center. Your approach might have changed my career path!’
“The latter has lead to the development of a 3-day introductory SD workshop for professionals.
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Cas
the level required to pass~ not surprising);
¢ a maximum of 70 students can take the same version of the exam due to seating constraints
in our main computer room.
However, developing such current, real-world cases especially the exam cases~ is difficult
and time-consuming: good cases need to be relatively simple and short (at least feasible by good
students in about 1 to 2 hours), actual and interesting, realistic in terms of boundaries / structures
/ behaviours, sufficiently interesting in terms of the link between structure and behaviour, useful
for proposing/testing policies, and perfectly tested and worded.
Hence, developing good cases is demanding for lecturers —especially in large-scale SD courses
for which many different exam cases need to be prepared4] It may therefore be desirable for
university lecturers of SD courses around the world to join forces, start up a small network, and
start exchanging the most relevant real-world testing/teaching cases (and underlying models and
answers to the questions), or to submit their SD cases as papers to the International Conference
of the System Dynamics Society.
2 Using Real-World Cases for SD Teaching at Delft Uni-
versity of Technology
Many SD courses taught all over the world use good but voluminous books like (Sterman_2000)
or (Ford 1999), publicly available online resources (e.g. Road Maps), or package-specific resources
(e.g. Vensim’s User and Modeling Guide, Pow ials,...). But the exercises available
there are mostly didactic in nature, style and size.
Until 2007, most exercises and cases used in the introductory SD courses at Delft University
of Technology were didactic too, whi sufficient for the first and the third learning goals of
the introductory system dynamics course:
wa
1. to have basic knowledge of SD as a field, philosophy, theory to link dynamic behaviour to
underlying (stock-flow and feedback) structures, and methodology for constructing models
(scientific method applied to dynamic modelling);
2. to be able to apply the SD method to cases of intermediate complexity using SD software
packages ~ in other words, being able to translate dynamically complex issues into causal
loop diagrams, stock-flow diagrams and SD simulation models, and to test and use them for
policy design and advic
3. to have a basic under:
proce
and of the use and possible contribution of SD modelling within the
of problem solving™)
However, the second learning goal was —before 2007- insufficiently dealt with.
Most lecturers at Delft University of Technology’s faculty of Faculty of Technology, Policy
and Management (try to) use actual real-world cases. Such ‘hot cases’ allow to arouse intere:
of students and show them the real-world applicability (and hence the relevance) of the methods
taught. All new exercises and cases developed for the introductory SD courses relate from 2009 on
to actual and important issues too. Almost all of the exercises and cases used in the introductory
SD course taught nowadays at Delft University of Technology are hot cases, That allows to
address additional essential skills for SD modellers (see also (Meijer, Pruyt, and Slinger 2010): to
4Over the last year, the author had to develop eight different testing/teaching cases for different exam sess
of the introductory SD course at Delft University of Technology.
5SD as an approach to consulting so as to achieve client confidence and acceptance is more thoroughly addressed
in follow-up cours
©Several of these hot cases have been submitted for presentation and publication to the International System
Dynamics Conference, all of which have been accepted.
ions
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Cas
be able to recognise when and in what form SD may be an appropriate method for particular real-
wold issues, to translate dynamically complex issues into useful SD models, and to test and use
them for realistic policy design and real-world advice ~ as such addressing the second learning goal.
Today, the main building blocks conveyed in the introductory SD course therefore relate to:
« model building: students learn how to proceed iteratively towards conceptual and fully spec-
ified SD simulation models ~ according to and respectful of the SD philosophy /methodology;
model structures: (generic and specific) Stock-Flow and Feedback Loop structures, simple
to complex delay structures, lookup/graph functions, other useful functions (min, max, sin,
step, ctc.), and tips/tricks related to software packages;
understanding of the link between structure and behaviour: the understanding of the link
between structure and behaviour is gradually sharpened (and in the end heavily tested by
means of most of the 20 rather difficult multiple choice questions on the exam);
qualitative conceptualisation and analysis, and model communication: students learn how
to make extensive and aggregated Causal-Loop and other diagrams for distinct purposes
(conceptualisation, analysis and communication);
e model use: different model uses are illustrated.
3 Some Old and New Hot Teaching/Testing Cases
Publicly available ‘hot teaching/testing cases’ developed and used at Delft University of Technology
include among else:
* the purely qualitative Dutch Soft Drugs case (see for the case description)
* the Cholera in Zimbabwe case (see (Pruyt 2009a)for the case description);
« asimplistic Electrical Vehicles Boom - Lithium Scarcity case (see (Pruyt 2009c) for the case);
« the Redevelopment of Dutch Social Housing Districts case (based on and
presented as a case in (Pruyt 2009¢));
© the Fall of the Fortis Bank case (s\ for the
For more information on, and more examples of, ‘hot’ teaching/testing cases see (Pruyt 2009c),
and for all currently used teaching cai (Pruyt 2010a). Most of these publicly available
cases actually require intermediate modelling skills. Students need to have some modelling ex-
perience/practice in order to be able to deal with the:
challenged by them: hence the need for more introductory
Following four cases —developed between April 2009 and March 2010- are therefore presented here:
se description).
as
but not too much in order to be
‘sas well as more advanced cases
the Chinese Pneumonic Plague case (sce section|4)and appendix|A), which is easy and short;
for
the Mexican Flu case about the (A-HIN1)v pandemic (sce section [5] and appendix
the case, and (Pruyt and Hamarat 2010b) for a more thorough analysis), which is easy but
lengthy;
® the Concerted Run on the DSB Bank case (
(Pruyt and Hamarat 2010a) for a deeper analys
by most students as rather) difficult;
tion 6|and appendix [C| for the case, and
, which is relatively short but (perceived
e the Rare Minerals/Metals case (see section|7, appendi and —for a better model about the
e- (Pruyt 2010b)) which is very long and also very difficult (at least for an introductory
SD course of about 35 to 42 contact hours and part of a 3-hour exam).
iss
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Cas
These cases are briefly presented and discussed below in incre:
descriptions and case questions are available in the appendix”,
sing order of difficulty. The case
The following four ‘hot’ cases sing order of complexity— were also developed and used
for testing purposes between April 2009 and March 2010, but are not included in this paper since
they may still be useful for testing purposes at Delft University of Technology:
e the Northern Bluefin Tuna Fisheries case related to overfishing of North-Eastern bluefin
tuna and the (in)effectiveness of ICCAT policies (relatively easy);
e the Radical
tremist activ
on/Deradicalisation case about the evolution towards harmless and/or ex-
m (rather lengthy and difficult);
« the Transition towards Sustainable Energy Systems case about spreading/concentrating sub-
sidies for innovative renewable energy technologies (rather lengthy and difficult);
the Food Security versus Energy Security case about potential food scarcity in case of chronic
fossil fuel scarcity and without a large-scale transition from first to second generation biofuels
(based on (Pruyt 2008b)) (very lengthy and difficult ~ further bridging the gap with the SD
project case).
4 Case 1: Pneumonic Plague in China
The case presented below used as an exam case in August 2009 for a group of 20 BSc students dur-
ing their time-constrained double-course exam of the introductory SD course and the introductory
differential equations course. The case is about half the size and about half as difficult as a regular
introductory SD exam (to compensate for the double-course aspect of the exam). Students found
this case easy. Most students were familiar with epidemiological modelling since most of them
solved the ‘Cholera in Zimbabwe’ case during one of the computer labs. The Preu-
monic Plague case description can be found in appendix{Alon page|22] It is included in the SD exer-
cises book as an exercise at the end of the ‘easy SD questions’ chapter. The basic Pneumonic Plague
is available at |http://forio.com/simulate/simulation/e.pruyt/lungpest-in-china).
model is
[Case questions 1 and 2:] First students are required to make a simple System Dynamics
simulation model (see Figure|I{a)) of a local pneumonic plague epidemic, as well as a corresponding
complete ‘causal loop diagram’ (sce Figure [I{b)).
[Case question 3:] They need to simulate the model and make graphs of the evolution of the
infections, the deaths, the recovering population, and the deceased population (see Figure{I{c)).
[Case question 4:] Then they need to extend the model to take the social dynamics during an
outbreak of an extremely contagious and lethal illness such as pneumonic plague into account: in
this case that means an automatic drop in the contact rate caused by illness and anxiety (see Figure
(2{a)), and make graphs of the evolution of the infections, the deaths, the recovering population,
and the deceased population (sce Figure [2(b)). They also need to recognise that the dynamics
changes a little bit, but that this does not change the overall picture.
[Case question 5 and 6:] Students then have to validate the model and test the sensitivity of
the model for small changes in the normal contact rate, the impact of the infected fraction on the
contact rate, and another variable of choice.
[Case questions 7 and 8:] Finally they need to test whether an increasing supply of antibiotics
leads to a lower number of fatalities (see Figure [2(c)) and whether the epidemics can be stopped.
Building blocks addressed in this 1 loop diagram-
ming of aging chains, formulating special functions (lookup functions and time series), and explor-
ing model and policy behaviour.
se include stock-flow modelling and caus
7 The corresponding SD models and answers will be sent upon request to colleagues willing to exchange ‘hot’
cases. All models are available in Vensim and in Powersim formats, all cases are available in Dutch and English.
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Cas
total population
_
*
susceptible infected [I recovering
; population
population re weeg eas population
inital total recovery ime
population
~~
f\. ratio [ldeaths «fatality ratio
contact rate
deceased antibiotics coverage of
population the population *
(a) Stock-Flow Diagram of the basic Pneumonic Plague model
recovering and
recovered —*
md
infection ratio recoverings
oS \
von Selig ratio
susceptible ow A=) infected population
ch depleting the infections ie
population“ suscepable infection loop \
A a. \
infected fraction festa ioe =)
contact rate bs i
. + antbio
total population 2) coverage of
concentration loop * =
the population
= deceased
population
(b) Causal-Loop Diagram of the basic Pneumonic Plague model
40,000 persons/Month
10,000 persons
20,000. persons/Month
5,000 persons
0. persons/Month
0. persons
Time (Week)
infections : LungPest] persons/Month
deaths : LungPestl persons/Month
recovering population: LungPestl. ——________________ persons
deceased population : LungPest)., ———____________—. persons
(c) Behaviour of the basic Pneumonic Plague model
Figure 1: SFD, complete CLD and behaviour of the basic Pneumonic Plague model
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Cas
impact infected
normal contact population on contact
rate pcr
‘« infected fraction
contact rate
susceptible infected recovering
population | i ¢-ions Population recoverines | Population
initial total ry repovery
Population fection ratio on
deaths «fatality ratio
deceased antibiotics coverage Of 4g time
population the population
(a) Stock-Flow Diagram of the extended Pneumonic Plague model
20,000 _persons/Week
10,000 persons
10.000 persons/Week
5,000 persons
0. persons/Week
0 persons
0 | 2 3 4 5 6
Time (Week)
infections : LungPest2 persons/Week
deaths : LungPest2 persons/Week
recovering population ; LungPest2. ———____________— persons
deceased population : LungPest2. ———____________——. persons
(b) Behaviour of the extended Pneumonic Plague model
20,000 persons/Week
10,000 persons
10,000 persons/Week YA
5,000 persons F
0. persons/Week %
0. persons
0 1 2 3 4 5 6
Time (Week)
infections : LungPest2Policy, ————____________—— persons/Week
deaths : LungPest2Poliey, ————— persons/Week
recovering population : LungPest2Policy, —__________—_ persons
deceased population : LungPest2Poley —————_________— persons
(c) Behaviour of the extended Pneumonic Plague model in case of a linear increase
of the antibiotics coverage
Figure 2: SFD and behaviour of the extended Pneumonic Plague model, without/with supply of
antibiotics
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Ca
In teaching, this case is used at the end of week 2 (see curriculum in (Pruyt et al. 2009)) or
at the end of day one of a three-day workshop.
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Cas
5 Case 2: Mexican Flu
Exploratory SD models of the spread of the new (A/HIN1)v flu variant ~also called Mexican flu
or swine flu- were developed several days after the first signs of the outbreak of a new flu variant
in Mexico. Several months later, the models were used to make a good hot teaching/testing case
for BSc and MSc students. The case is good because of the step-wise approach and the familiarity
of students with the topic.
At Delft University of Technology, the case was given in August 2009 to about 25 BSc students
during their time-constrained retake exam of the introductory SD course and in October 2009 to
about 35 MSc students during their time-constrained exam. Students found this case relatively
easy to solve but complained about the amount of time allotted (3 hours for answering 20 Multiple-
Choice Questions as well as this case). Nevertheless, students performed —in general very well on
this
The Mexican Flu case description can be found in it Soa
ase.
on page [23] The model is
ESDMA for informed crisis
model is available at /http://forio. com/simulate/simulation/e.pruyt, mexican-f1ul
[Cas 3:] First, students need to make a very simple simulation model about a
flu epidemic in the Western world (see Figure B(a)), construct a complete CLD of the simulation
model (see Figure|3{(b)), simulate its behaviour and draw graphs of the evolution of the susceptible
population, the infections, the infected fraction, and the recovered population (sce Figure [3{c)).
[Case questions 2.1-2.2:] Second, students need to extend the simple model displayed in Figure
(Bla) with a form of seasonal immunity. Although the extension is rather small, an additional flow
(with a well-thought-out formulation) and a time series or sinus function are required.
Students are asked to adapt the model and simulate it (see Figure [a)), draw graphs of the
evolution of the susceptible population, the infections, the infected fraction, and the recovered
population (see Figure [A{b)), and compare the outputs of this model with the outputs of the
previous model. The epidemic now occurs later and is ‘atastrophic.
[Case questions 3.1-3.2:] Third, students are asked to duplicate the model and turn it into a bi-
regional model comprising the Western world as well as the densely populated Developing World
(see Figure [5{a)). Again, students are asked to simulate the model, make graphs of the evolution
of the susceptible population, the infections, the infected fraction, and the recovered population of
the Western World (see Figures [5{b) and [5{c)), and compare the graphs of the Western region
with the previous ones. Students are expected to note that an early outbreak in the Developing
World —because of a higher contact rate and a higher infection ratio in the Developing World—
may actually lead to an early outbreak in the Western World, but with a lower infected fraction,
followed by a more intensive outbreak in winter (when immunity is lower).
[Case questions 3.3-3.4:] Then students are asked to validate the model, investigate the sen-
sitivity of the infected fraction of the Western World to small changes of contact rate, infe
ratio, and recovery time of the developing world (see Figure(6(a)), and draw conclusions. Possible
conclusions are that the infected fraction may not reach the feared third of the population, that
the precise outbreak in the developing world may actually lead to a weaker or stronger second
peak in the Western world, and that the size of the second peak is inversely proportional to the
size of the first peak (which is not the case for other sets of parameter values).
[Case question 3.5:] Students are also asked to investigate what happens
infected population in the Western World if a vaccine becomes available in month 6 and 50% of
the Western population gets vaccinated almost immediately after the vaccine has been developed.
in terms of the
5The flow between these populations, the net ‘susceptible to immune population flow’ is equal to: (‘normal
immune population’ - ‘immune population’) /‘susceptible to immune population delay time’, but the flow cannot
be greater than the ‘susceptible population’ divided by the ‘susceptible to immune population delay time’ if there
is a net flow towards the immune population, and the return flow cannot be greater than the ‘immune population’
divided by the ‘susceptible to immune population delay time’ if there is a net flow towards the susceptible population.
10
Vew Hot Teaching/Testing Case:
Pruyt, 2010. Making System Dynamics Cool II:
total population,
ce te recovery time
susceptible VA ped
lat
Eanes infections population | recovery (| Population.
contact rate infection rate
(a) SFD of the first version of the simulation model of the Mexican Flu case
total population
b recovery time
infection fraction
draining the
+ Susceptibtes
“infection . . draining the
loop Toop infected loop
ee infections miogted recovery —p-Tecovered
4“
- KU
infection rate
contact rate
(b) Complete CLD of the first version of the simulation model of the Mexican Flu case
800M. person
04 Dmnl
400M _ person
0.2 Dmnl
°
person
susceptible population : S1b
infected population: S1b 2-
recovered population: Sib. —— ++ —+— +
infection faction: SIb = ~~
(c) Behaviour of four key variables for the first version of the Mexican Flu model
on of the Mexican Flu model
SFD, complete CLD, and behaviour of the first. ve
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Case: u
contact rate inféctionrate recovery time
Ne
susceptbe ¥ are recovered
population
Beas al recovery uP
‘a infection faction
susceptible to immune a Ls a
population fow ‘otal population.
susceptible to immune
population delay time | inmnune
population
population “€— normal immnc
population fraction
simulation model of the Mexican Flu c:
(a) SFD of the second version of the
400M. person
004 Da oe
200M_ person aa
susceptible population : $23 person
infected population: $23. BB 8 Bab person
recovered population : $23. ——3-— + —4— —4—-3—-— person
Dmnl
copie
infection fraction : $23. --—
Se ee et
(b) Behaviour of four key variables for the second version of the Mexican Flu model
ion of the Mexican Flu model
Figure 4: SFD and beha
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Cases 2
infection fucion contact rate WW
a. recovery tie
interregional
contact rate>
inti s ww | SoERRBE oi
inetions WW <inecton racéon
ww>
“a Se sheoiteen we inosonmte DCs recovery tine DCs
= ww a comtamsTaie DCE interregional
‘susceptible to immune » ™S
population fow WW tots poplin,
~ ww Fecoyered |
ee ad inital S DCs = Bega
Soomafirmite sppnalinmmne - recovery DCs
susceptible to imme Bopuation WW on Gntin WW ATI / _
populason delay tine WIV y ‘<a
Des
susceptible to immune Seg
population fow DCs ‘otal popuiation
Ne Des
ao -
Lapses ‘normal imme
susceptible tine opuiaton DCS on Baton DCS HE
population delay ime DCs
(a) SFD of the third version of the simulation model of the Mexican Flu
400 M_ pesson
0.2. person/contact
200M. person
0.15 person/eontact
0.02 f
_ : /\
0.1 personicontact ¥ 001 | \
susceptible population WW :S4 person ANE,
infected population WW : 84 om “person 6 9
recovered population WW :S4 =" person Tene (Month)
infection rate WW: 84-6 = 4 personleontact eon gacton WW S4
(b) Behaviour of four key variables for the third version of the Mexican Flu (c) Detail: the infected fraction
model
Figure 5: SFD and behaviour of the third, bi-regional, version of the Mexican Flu model
Figure 6{b) shows that one of the consequences for the infected population in the Western World
is the elimination of the second outbreak.
[Case question 3.6:] Finally, students are asked to formulate a 1-sentence policy recommenda-
tion to the European Commission concerning this flu and what to do about it. Students could
then for example conclude that: If a vaccine can be made before the second peak, then a heavy
first outbreak should be avoided (c.g. by taking the necessary social measures), but if a vaccine
cannot be made before the second peak is likely to occur, then it would even make sense to amplify
the first peak (e.g. by organising flu parties).
Building blocks addressed in this include stock-flow modelling and causal loop diagram-
ming of aging chains, formulating special functions (lookup functions, time series and/or sinus
functions, MIN/MAX functions, well-thought-out flows), and exploring different model and policy
behaviours.
In teaching, this case is used at the end of week four (see curriculum in (Pruyt et al. 2009))
or at the end of day two of a three-day workshop.
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Case:
infection fraction WW
0.04
0.03
0.02
0.01
infection fraction WW : SS
infection fraction WW : SSInfectionFractionDCs20 a 2 a
infection fraction WW : SSInfectionFractionDC 310, —3 —
infection fraction WW : SSContactRateDCs200 —-—-4-—-—- ~~
infection finction WW : SSDoublRecoveryTime —--—---§--—-—---5
infection fraction WW : SSHalfRecoveryTime °
13
(a) Sensitivity of the infected fraction of the Western World to changes in the infected fraction of the Western World
to small changes of contact rate, infection ratio, and recovery time of the developing world
infection fraction WW
0.0225
0.0169
E 0.0112
A
0.0086
0
0 3 6 9 12 18 21
Time (Month)
infection faction WW : SS§_-+—+}—+—+—+—+—+—
infection fraction WW : S5Policy -2
(b) Effect of sufficient vaccination before the second flu peak
Figure 6: Sensitivity and policy analyses
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Cas “4
6 Case 3: The Concerted Run on the DSB Bank
An exploratory SD model of a concerted bank run was developed on 1 October 2009, right after
Pieter Lakeman’s call for a run on the DSB Bank. This small, simple, high-level, fast-to-simulate
model was used at that time for the purpose of exploration, more precisely, to quickly foster
understanding about the possible mechanisms and dynamics of concerted bank runs, to test high-
level policies to prevent such bank runs from succeeding, and to test and teach SD students.
The case was given in January 2010 to about 70 BSc students and in November 2009 to about
25 first-year MSc students during their time-constrained introductory SD retake exam at Delft
University of Technology. All Dutch students were already familiar with the highly mediatised
run on the DSB Bank. Students even guessed —while d potentially interesting exam
cases during the'final lecture— this would be.an,exam ease. Moreover many students had already
modelled the similar Fortis Bank case during the computer labs. And although this is smaller
than most hot teaching/testing cases, students found it rather demanding because of the lack of
a step-wise approach and somewhat difficult formulations.
The DSB Bank Run case description can be found in appendix (Clon page 25) The model is
explained and explored in depth in (Pruyt and Hamarat 2010a), is available and can be simulated
at http: //forio.com/simulate/simulation/e.pruyt/dsb| and is used briefly for ESDMA in
case
perceived likelihood
aEING Paik Gattae bank fBiture risk
declaration
/. perceived likelihood . .
solvency faire credibilty denials
© Sevdiauitlny ime: credibility
DSB
liquid ftaction expected hindrance
ruming possible bank faihire
perceived likethood DsB coasccted igual
liquidity ire Organs it~" 9 gachon at ages
concerted
total asset total ae
kabilty ratio Q
es
new fixed loan peas
new fixed loan as Ps
faction oflig lost Se
ied || Iqud
liquid asset deposits |} deposits —,
liability ratio X and loans || and loans epee
: withdrawal time
OSH anid assets fixed assets
new nee asse’s Pi iguidation
© Xeew ined Ay. liquidation losses
new deposits and |! tiquid asset iat
ae i Byuidation
ae loans fability target premium ¢}
liquid assets lost iquidation time
Figure 7: Aggregated structure of a ‘concerted bank run’ SD model
[Case question 1:] First, students need to make a simulation model based on the case descrip-
tion. The SFD of the SD model is displayed in Figure |7| Since the model is a short-term crisis
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Cas 15
model, it is assumed that (i) there is no change in assets due to profit accumulation, (ii) fixed and
guaranteed deposits and loans do not come at terms, (iii) there are no net shifts from liquid t6
fixed assets, nor from liquid to fixed deposits and loans. Note that soft —but pos i
aspects like anger and expected hindrance from bank failures are explicitly modelled.
liquid deposits and loans lost perceived likelihood bank failure risk
° 6 2 8 4 30 36 2
Time Day)
Sa ent ot 0 momo
{fod Govan ot ESD sesane range Ra in ae: DAB sec
Figure 8: Behaviour of different scenarios for the ‘concerted bank run’ model
[Case questions 2, 3, 4:] Then students need to use to model to simulate distinc
Figure |8| shows the behaviours of 4 scenarios on two important variables: the liquid depo
loans lost and the perceived likelihood of a bank failure. The DSBO scenario (displayed in green)
shows that —with this model and these parameter values (anger amounting to 50%, expected
hindrance of a bank failure to 50%, and a liquidation premium of 15%)- nothing happens without
a call for a bank run. The DSB1 scenario (displayed in blue) shows that with a concerted bank run
lasting two days, 50% anger, 50% expected hindrance of a bank failure, and a liquidation premium
of 15%, the initial concerted run is followed by a relatively long period of liquid deposits and
loans losses reducing the liquid assets (being replenished by liquidation of fixed assets), before the
bank suddenly collapses. The DSB2 scenario (displayed in orange) shows that thi
sooner with a liquidation premium of 25%. And the DSB3 scenario (displayed in red) shows that
the concerted bank run is followed immediately by a full collapse of the bank in case of 100%
anger, 100% expected hindrance of a bank failure, and a liquidation premium of 25%.
Although the modelled bank seems to collapse sooner or later after an initial perturbation of
sufficient amplitude, the delay with which the second run follows upon the concerted run makes
a big difference for those involved: in scenarios DSB1 and DSB2 there seems to be some time
for strategies/policies and anticipative crisis management, but not in scenario SDB3, in which
the second run follows immediately upon the first run, in which case there may only be time for
reactive crisis management or an ‘emergency measure’ to place the bank under legal restraint.
The strange ~at least for continuous systems models~ peaks in liquid deposits and loans lost
arise because the stock of liquid deposits and loans is depleted.
[Case questions 6 and 7:] After briefly validating the model, students need to draw a causal
loop diagram to communicate the main feedback loops and explain the link between structure
and behaviour: the positive liquidity and solvency loops in Figure [9] make that —unless actively
stopped- the likelihood of a bank failure keeps on increasing until the bank effectively collapses.
[Case question 8:] Finally, students need to design and test policies to prevent the bank from
collapsing. Possible policies include inflows into deposits and loans, especially into the fixed de-
posits and loans, generated (for example) by raising the interest rate on those products, or by
liquid assets through new equity (both policies are depicted in red in Figure [7).
Building blocks addre
ming of highly aggregated structures, formulating special functions (lookup functions, time series
and/or double step functions, MIN/MAX functions, well-thought-out flows), and exploring differ-
behaviours.
d in this case include stock-flow modelling and causal loop diagram-
ent scenario and policy
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Cas
credbility denials aroes Peele Bt
SS, faction
running
anger
al oe
srceived percered
16
lihood Frettiood liquid iad éxposis hindrance bank
eeney Soo. ) oy Tansloat failures
solvency +
‘failure concerted liquid
teen as fiaction ruming
liquid assets lost
liquidation
premium
liquid assets
Figure 9: (Aggregated) Causal-Loop Diagram of the concerted DSB Bank Run Case
In teaching, this case is used at the end of week four (see curriculum in (Pruyt ct al. 2009)
or at the end of day two of a three-day workshop.
7 Case 4: Chasing Rare Minerals/Metals?
The Rare Earth Metals case presented below was inspired by the first of a series of four articles
in Dutch newspapers about scarcity of Minerals/Metals.
The
time-constr
was used on 19 January 2010 to test 15 MSc and 60 BSc students during their
ined introductory SD exam at Delft University of Technology. Almost all students
found thi xtremely difficult because (i) all variables are looped (which means that students
using Powersim get error messages in all variables until all problems are solved), (ii) the case is
slightly larger than most teaching cases, (iii) more special functions (lookups, time series, Min/Max
functions, ete.) need to be formulated, and (iii) the wording was/is not perfect.
The case description can be found in appendix [D]on page|27| A much better but larger and
more complex- SD model related to this topic is described and used in (Pruyt 2010b).
[Case questions 1.1 and 1.2:] First, students need to make an incomplete simulation model
about the extraction/use/recycling of these metals (see Figure{I0(a)), and draw a detailed causal
loop diagram of this incomplete model (sce Figure [10{b))
[Case question 2.1:] Then students are asked to complete the simulation model by adding
structures and variables related to the intrinsic demand, price-driven demand, the demand for
recycling, etc (see Figure(11), to simulate the model, and make graphs of the expected price-driven
demand, the relative price, the reserves, and an output indicator fraction supplied of intrinsically
demanded (sce Figure (12).
[Case questions 2.2 and 2.3:] Then students need to validate and test the sensitivity of the
model (more specifically the fraction delivered of intrinsically demanded and the reserves) for
small changes in the price effect supply shortage, the initial reserves, and the fraction available of
desired recycling.
[Case questions 2.4 and 2.5:] Finally, students are asked to make an aggregated CLD to show
the main feedback loops (see Figure |I3), and explain the link between structure and behaviour.
Building blocks addressed in this case include stock-flow modelling and causal loop diagram-
ming of aging chains and recycling structures, formulating (too) many special functions (lookup
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Cases 17
expected price driven metal X used
demand for metal X and lost
Joss non recycled
metal X recyeling fraction
metal X
extraction time production time metal X average Etim
dil eaceves) “IX containing products ay of metal X in use
metal X } metal|X in se
reserves amount of
pet =p>| supply ; P| metal Xin
‘cialis mes metalX | production metal X | "tse
See ae non ge. containing products
\ amount of metal X
desired extraction to recycling
metal X recycling time
metal X
amount of |initial amount of metal
metal Xin [3
supply recycled recycling in recycling
metal X
(a) Stock-Flow Diagram of the Incomplete Metal Scarcity Model
eieasiteas loss non recycled
mineral X
production time metal X
extraction time containing products = recycling
metal X fraction
metal X
ao * sapply ru of ‘/~ :
metal X +P apnea, ———— etal X in use average lifetime
reserves Ch extraction 4-) . F ( pitino
itietalX me 4+)
om ‘more recycling less ‘more recycling
extraction loop ‘i metal loop
desired extraction
peniree supply recycled /~ metal X in ‘metal X to
wy metal recycling recycling
expected price driven seoycting tive
demand for metal X mnetal X
(b) Detailed Causal-Loop Diagram of the Incomplete Metal Scarcity Model
Figure 10: Stock-Flow Diagram and Detailed Causal Loop Diagram of the Incomplete Metal
Scarcity Model
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Cases 18
extrapolated
demand rineral X
extrapolated increase is
demand mineral X
[ee) V4 demand mineral - ln,
desired recycling <Time>
mineral X
percentage increase ~~
demand mineralX __rebative ae level et fraction supplied of
desired recycling
‘rineral X
oupply shortage price
efitet mineral X
relative reeycting
‘cost mineral X
mninerale
fused but los
ry
relative exploitation
cost mineral X
recycling faction
Joss of non recycled mineral X
. Sreniaeee meal average lifetime of
piri hint Seam production time products. products containing
" Pan 7 containing mineral X suneran ee
a ee
mineral | mineral x | on serpy _|, saaminvotnmen 9 maximum reoyclable
mineral X “x. supplied for production i amount mincral X
A
desired exploitation paineral X to
‘pasta SE: mineral X pea time recycling be
supply mineral X bans
supply of recycled.
mineral X
Figure 11: Stock-Flow Diagram of the Metal Scarcity Model
ig) I y
1,000 Year
1 Dmoll
20 Dmnl
10,000 t /
/
0 Year
0 Dmnll i a
0 Dm A ps4
Z| Sb
ot
2000 2010 2020 2030 2040 2050
Time (Year)
expected price driven demand for metal X : metals. HHH Year
fraction delivered of intrinsic demand metal X : metals. ————HH4H4H4H4HH44H4H4H4H4H Dri
relative price metal X : metals Dmal
reserves metal X : metals t
Figure 12: Behaviour of the Metal Scarcity Model
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Cas 19
ees
4.
desired
recycling
reoyeled
metal
Figure 13: Aggregated Causal Loop Diagram of the Metal Scarcity Model
functions, time series, MIN/MAX functions, well-thought-out flows, delays, and avoiding simul-
taneous equations), exploring model behaviour, and aggregating and communicating complex
feedback loop structure:
In teaching, this c curriculum in (Prayt et al. 2009)
or at the end of day three of a three-day workshop.
e is used at the end of week seven
8 Conclusions, Lessons Learned, Proposal
All new testing/teaching cases developed over the last two years for the introductory SD course
at Delft University of Technology have been based on ‘hot’ issues.
Using ‘hot’ cases is a good way to enthuse students and to arouse their interest in applying
SD in case of real-world issues. Applying SD to ‘hot’ issues illustrates the relevance of SD for
dealing with real-world complex issues, which takes SD testing/teaching models one step further
than being didactically responsible exer
Although actual real-world testing/teaching are often more motivating, mostly they are
also more difficult than exercises developed in the first (and only) place to test/teach, because
they need to be sufficiently close to reality to be relevant.
Hence it helped to bridge the gap between the introductory SD course and the SD project
course by raising the level of difficulty of the introductory SD course. Now students learn all basic
SD modelling skills where they ought to learn those skills: in the introductory course.
However, developing relatively simple, actual, relevant, real-world testing/teaching cases
time consuming and difficult, especially when they need to be developed very rapidly in order to
very
be as ac
These ses have reinforced the reputation of the introductory SD course at Delft Uni-
versity of Technology of being difficult, but also clarified its relevance and goals. Consequently,
students seem to work harder and in a more focussed way, and with a side-long glance at the
actuality and real-world issues. After only 7 weeks, students are able to construct and use models
of real-world issues of a reasonable complexity, be it based on a precise description / specification.
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Cas 20
The use of ‘hot’ cases may well be the main cause of a significant improvement of the SD
modelling skills: although it is difficult to prove, it scems that the use of these testing/teaching
cases has accomplished more than the other measures discussed in (Pruyt et al. 2009).
In order to maximise the advantages and minimise the disadvantages of using ‘hot’ cases, it is
proposed to:
¢ start up a small (informal) network of university-level lecturers interested in sharing ‘hot’
testing /teaching cases,
e start exchanging cases bilaterally or by means of a central ‘case depository’,
© agree upon a set of criteria (e.g. hot) and a specific standard/format (c.g. italics for vari-
ables),
e respect authorship and correctly reference/cite (e.g. ‘developed by’ or ‘based on a case
developed by’) even for testing cases.
Regarding the cases discussed in this paper and provided in the appendix, it can be concluded
that:
The Pneumonic Plague case is a rather simple case which is appropriate a 1-1.5-hour exam
without multiple choice questions.
The Mexican Flu case is an interesting gradual, relatively easy case which is appropriate for
a 2-3-hour exam without multiple choice questions.
The concerted DSB Bank Run case is a relatively difficult case which is appropriate for a
2-2.5-hour exam without multiple choice questions.
¢ The scarcity of minerals/metals case is a difficult case which may be appropriate for a 3-hour
exam without multiple choice questions for good/intermediate/advanced SD students.
References
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Meijer, W., E. Pruyt, and J. Slinger (2010, July). Hop, Step, Step and Jump towards Real-World
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the 28th International Conference of the System Dynamics Society, Seoul, Korea. {I\ 3)
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[conferences '2009/proceed/papers/P1356.pdf| [4
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ics for Insightful Crisi
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Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Cas
22
APPENDIX — APPENDIX — APPENDIX — APPENDIX
A Pneumonic Plague in China
On 3 August 2009, an outbreak of pneumonic plague in north-west China was reported in the
media. The NRC Handelsblad (a Dutch quality news paper) reported the following:
Longpest duikt op in het noordoosten China
Dooranseredacte weteomchan | derd van de buitenwereld ‘behandeld binnen 48 uurbijnaal- man, diedezickte vervolgens via
ROTTERDAM, 3 AUG. De tiendui- \gpestwordtveroorzaakt tijd dodelijk,maartoedicning __‘hocstenop ‘den enande-
Eendinwonerstenhetchinces’ doordebaciereverielapest, dle vanandbioticabinnen 2Aunrna ren in sia omgeving overbracht.
dorpziketankunnengeenkant —_zichwaarschijnlijkook rond 1349 -_besmetting verlaagthetsterfte- Per contact is dekans op besmet-
op.Nadateenmanvorigeweck door Europay ie.De percentagetocongeyecr 15 pro- ting 75%,
oreioed aaa lone ides Tangdurigeepidemicénvande cent. ‘Volgens lokale bestuursteden
telijkezicktewerd ZwarteDood dooddetoencender- _. Eengroterprobleemvormtde _ gaathet dagelijks feven in Ziketan
Tantgestclabueltandercashed- deyandeburopescbevolling, besmctclikheld.Deaz4arige _ onertassen gewoon door. Deelf,
bende Chinese antoriteiten het Zo'nvaartzalhetnunictlopen, herder werd besmet doorcen. dleken tiggen intabieletocstand
dorpindenoordoostelijkepro- _zegtde Wereldgezondheidsorga- _knaagdicrofcenvio.Debacterle inet zickenhuis.Scholenen
vincie Qinghai volledigafgezon- -_nisatie, Weliswaarisde zickteon- _vestigdezichindelongenvande —_ openbategebouwen zijn open.
The BBC reported:
“A second man has died of pneumonic plague in a remote part of north-west China
where a town of more than 10,000 people has been sealed off. [...] Local officials
stern China have told the BBC that the situation is under control, and
that schools and offices are open as usual. But to prevent the plague [from] spreading,
have sealed off Ziketan, which has some 10,000 residents. About 10
other people inside the town have so far contracted the disease, according to state
media. No-one is being allowed [to] leave the area, and the authorities are trying to
track down people who had contact with the men who died. [...] According to the
WHO, pneumonic plague is the most virulent and least common form of plague. It
is caused by the same bacteria that occur in bubonic plague — the Black Death that
killed an estimated 25 million people in Europe during the Middle Ages. But while
bubonic plague is usually transmitted by flea bites and can be treated with antibiotics,
[pneumonic plague, which attacks the lungs, can spread from person to person or from
fatality
the authorities
animals to people], is easier to contract and if untreated, has a very high ca:
ratio.”
You are asked to make an exploratory
em Dynamics model of this outbreak. Use the
following assumptions: The total population of Ziketan amounted initially to 10000 citizens. New
infections make that citizens belonging to the susceptible population become part of the infected
population, which initially consists of just 1 person. The number of infections equals the product of
the infection ratio, the contact rate, the susceptible population, and the infected fraction. Initially,
the normal contact rate amounts to 50 contacts per week and the infection ratio to a staggering
75% per contact. The infected fraction equals of course the infected population over the
all other subpopulations. If citizens from the infected population die, they enter the stat
the deceased population, else they are quarantined to recover. The recovering could be modelled
cally as (1— fatality ratio) «infected population/recovery time. Suppose for the sake of
simplicity that the average recovery time and the average decease time are both 2 days. The fatality
ratio depends on the antibiotics coverage of the population which ~in this poor part of China~ is
(initially) 0%. As indicated in the article, the fatality ratio decreases from 90% at 0% antibiotics
coverage of the population to 15% at 100% antibiotics coverage of the population. Assume for
the sake of simplicity
because they are is really quarantined or because they they are not contagious any more.
sum of
s of
that the recovering population does not pose any threat of infection, either
1. Make a System Dynamics simulation model of a local pneumonic plague epidemics. Verify
the model.
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Cas 23
2. Make a ‘causal loop diagram’ of this model.
3. Simulate the model using a time horizon of a month. Make graphs of the evolution of the
infections, the deaths, the recovering population, and the deceased population.
4. The outbreak of an extremely contagious deadly illnes
causes the contact rate to drop (because of panick and illn
such as pneumonic plague actually
).
Adapt the model by closing the ‘loop’ between the infected fraction and the contact rate.
Create a function impact of the infected fraction on the contact rate that, multiplied with
the aforementioned normal contact rate (the one without epidemic and panick), gives the
effective contact rate. The function takes a value of 1 at an infected fraction of 0% 1, of 0.5
at an infected fraction of 10%, of 0.25 at an infected fraction of 20%, 0.125 at an infected
fraction of 30%, of 0.0625 at an infected fraction of 40% , of 0.03125 at an infected fraction
of 50%, and so on. Simulate the model over a span of 1 month. Make graphs of the evolution
of the infections, the deaths, the recovering population, and the deceased population. Does
this reduction of the natural contact rate the desired effect?
5. Validate your model. Propose 2 validation tests (except sen: is — see next
question), perform them, and briefly describe the results/conclusions.
6. Test (not too extensively) the sensitivity of the model for small changes in the normal contact
rate, the impact of the infected fraction on the contact rate, and one other variable of choice.
Briefly describe your conclusions.
7. Suppose that the antibiotics coverage of the population increases linearly in de first week of
the epidemics from 0% to 100%. What is the consequence on the deceased population?
8. Could the epidemics be stopped? Explain based on the structure of the model.
B= Mexican Flu
Mexican flu epidemic or pandemic: does it matter?
Let's go several months back in time to the moment the WHO reported the first signs of the
Mexican flu outbreak. Suppose that the European Commission asked you at that time to make
an experimental System Dynamics model related to the potential evolution of the Mexican Flu
(also known as A/HINI or swine flu) in the Western World.
Model and analyse the Mexican flu, first as an epidemic in the Western World, and then, as
a worldwide epidemic or pandemic in the Western World and the densely populated part of the
developing world. Keep in mind during your analyses that the Western World was especially
concerned about potential disruptions of society and economy if more than 30% of the active
population simultaneously has the flu.
B.1 Mexican flu as an epidemic in the Western World (_ /7.5)
Infections make that people from the
get the flu and migrate from the su
eptible population (initially equal to 600.000.000 persons)
ptible population to the infected population (initially equal
to 10 persons). The number of infections equals the product of the susceptible population, the
contact rate, the infection ratio, and the infected fraction. The infected fraction equals the infected
population divided by the total population. The average infection ratio of this flu variant in the
Western World was estimated at that time to amount to 10% infections per (close) contact.
Suppose that the contact rate in de Western World amounts to 50 (close) contacts per person per
month.
Members of the infected population flow after an average recovery time of 2 weeks to the
recovered population (initially empty). Assume for the sake of simplicity that the entire infected
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Cas 24
population recovers (although feared at first, there are, relatively speaking, not that many swine
flu deaths).
1. ( /3) Make a System Dynamics simulation model in Powersim of Vensim of the epidemic
described above. Verify the model.
2. ( /3) Make a complete causal loop diagram of this simulation model.
3. (/1.5) Simulate the model over a period of 4 years. Make graphs of the evolution of the
susceptible population, the infections, the infected fraction, and the recovered population.
B.2 What if not everyone in the Western World is infected? (_ /5.5)
It is likely that not everyone gets this flu, just like in case of the normal flu. That probably
means that there is apart from the susceptible population— also an immune population. Adapt
the previous model.
Set the susceptible population in the Western World initially to 330.000.000 persons and the
immune population to 270.000.000 persons. However, there is also a seasonal dynamic between
both populations: the susceptible population grows towards the winter season, and the immune
population grows towards the summer season.
The flow between these populations, the net ‘susceptible to immune population flow’ is equal
to: (‘normal immune population’ - ‘immune population’) /‘susceptible to immune population delay
time’, but the flow cannot be greater than the ‘susceptible population’ divided by the ‘susceptible
to immune population delay time’ if there is a net flow towards the immune population, and the
return flow cannot be greater than the ‘immune population’ divided by the ‘susceptible to immune
population delay time’ if there is a net flow towards the susceptible population. Suppose that the
‘susceptible to immune population delay time’ amounts to 1 month.
The normal immune population is equal to the product of the total population and the normal
immune population fraction. This normal immune population fraction fluctuates between 30% in
month 0, to 70% in month 6, to 30% in month 12, to 70% in month 18, and so on.
1. ( /3.5) Extend the simulation model as described above.
2. ( /2) Simulate the model over a period of 4 years. Make (on your computer and on your
exam copy) graphs of the evolution of the susceptible population, the infections, the infected
fraction, and the recovered population. Compare these graphs with the previous ones: briefly
describe the differenc
B.3. The Mexican flu as a worldwide epidemic (or pandemic)? ( /12)
(Remark: You can model the description in this subsection, even if unsuccessful in subsection |B.21]
The flu epidemic in the Western World may be strongly influenced by the development of the
flu in densely populated Developing Countries. Make therefore a similar submodel for a second
region, namely the densely populated part of the third world. There are some small difference
Suppose that the average contact rate in this second region amounts to 100 (close) contacts
per person per month. The infection ratio is probably slightly higher, namely 15% or 0.15 in-
fections per contact. The susceptible population of this region amounts initially to 2.000.000.000
he immune population to 1.000.000.000 persons, and the infected population to 100 per-
populated regions are not modelled here because they are causally less important
to an outbreak of the flu.] The majority of these countries are located in the Southern hemisphere,
and their populations generally have a lower immunity: the normal immune population fraction
amounts therefore to 30% in month 0, 10% in month 6, 30% in month 12, 10% in month 18, and
so on.
There is of course also contact between these regions (the Western World and the densely
populated Developing Countries). Suppose that the interregional contact rate amounts to 0.1
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Cas 25
(close) contacts per person per month. Add an additional term to the infections variables of both
regions. In case of region 1, this additional term may look like: + ‘susceptible population region
1’ x ‘interregional contact rate’ x ‘infection ratio region 1’ x ‘infected fraction region 2°
1. ( /4) Extend the simulation model as described above.
2. ( /1.5) Simulate the model over a period of 4 years. Make (on your computer and on your
exam copy) graphs of the evolution of the susceptible population, the infections, the infected
fraction, and the recovered population of the Western World. Compare the graphs of the
Western region with the previous ones: briefly describe the differences.
3. ( /1) Validate the model: propose 2 validation tests (except sensitivity anal:
them, and briefly describe the resultats/conclusions.
is), perform
4. ( /3) Investigate the sensitivity of the Western World submodel to small changes of contact
rate, infection ratio, and recovery time of the Developing Countries. Test for example a
contact rate in region 2 of 200 (close) contacts per person per month. Describe briefly what
you can conclude from these analyses in terms of the infected fraction of the Western World.
5. (_ /1.5) Suppose that a vaccine becomes available in month 6 and that 50% of the Western
population gets vaccinated in no time. What is the consequence in terms of the evolution of
the infected population in the Western World?
6. (_ /1) Formulate a L-sentence policy recommendation concerning this flu and what to do
about it to the European Commission.
CA Concerted Run on the DSB Bank
Over the last year, newspapers have been reporting about many bankruptcies of banks and financial
institutions. The latest bankruptcy of a Dutch bank, the Dirk Scheringa Bank or DSB, is a very
special case, because the bankruptcy was actually caused by a concerted bank run by angry clients
following the call by Pieter Lakeman to empty their deposits.
Since you already modelled the fall of the Fortis Bank, you are asked by the Dutch central
bank ‘De Nederlandse Bank’ to model the fall of the DSB. Keep in mind that a crisis model is
not the same as a complete bank model for going concern.
Deposits being emptied are —from the point of view of a bank~ liquid deposits and loans lost.
These liquid deposits and loans lost drained the liquid deposits and loans, which initially amounted
to €4,500,000,000.
Liquid assets lost are equal to the liquid deposits and loans lost bet
ing system. Liquid assets lost decrease the amount of liquid assets, which initially amounted to
€1,150,000,000. Suppose that there is a liquid asset liquid liability target of 20%, which means
that fixed assets, which initially amounted to €4,600,000,000), need to be liquidated and turned
into liquid as.
use of the double account-
if less than 20% of liquid deposits and loans are covered by liquid assets. Suppose
that the liquidation time is only 1 day, which means that there are enough interested parties to
almost instantly sell < to. However, given this haste, there is a liquidation premium of 10%
on these emergency sales. In other words, only 90% of the fixed asset value is turned into liquid
sets in these emergency sales, and 10% of the fixed asset value is lost as liquidation losses. Keep
in mind when you model the liquidation flow that the model you make is a crisis model and not a
complete banking model: there should at most be a net flow from fixed assets to liquid assets, but
not the other way around. Apart from the liquid deposits and loans, DSB also had fixed deposi
and loans worth €1,000,000,000 which remained constant during the crisis because fixed depos
and loans cannot be emptied by depositors or lenders before their due date.
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Ca 26
In a normal bank run, the amount of liquid deposits and loans lost equals the liquid fraction
running away away times the liquid deposits and loans divided by the withdrawal time. However,
two factors amplified the running away effect in the case of DSB crisis: clients were angry because
of unacceptable sales pr
ices and the mediatised unwillingness of the bank to compensate the
victims of these prac and people understood the hindrance of a bank failuré® after having
witnessed bankruptcies of several banks over the past few months. Multiply the previous right
hand side of the equation therefore with following two factors: (1+hindrance of bank failures) and
(1+anger). Suppose that the hindrance of bank failures amounts to 0.5.
Since the DSB bank run was actually to some extent an organised bank run, you have to
add an additional term to take this concerted action into account, for example: concerted liquid
fraction running away times liquid deposits and loans divided by withdrawal time of 1 day. And
do not forget that the maximum amount of liquid deposits and loans lost equals the amount of
liquid deposits and loans divided by the withdrawal time.
Suppose that the liquid fraction running away amounts to 0% if the perceived likelihood of a
bank failure is 0%, that it amounts to 0% if the perceived likelihood of a bank failure is 25%, that
it amounts to 1% if the perceived likelihood of a bank failure is 50%, that it amounts to 10% if the
perceived likelihood of a bank failure is 75%, and that it amounts to 50% if the perceived likelihood
of a bank failure is 100%.
The perceived likelihood of a bank failure may be modelled as (100% - credibility of the denials)
times the maximum of either the perceived likelihood of a liquidity failure or the perceived likelihood
of a solvency failure.
ived likelihood of a liquidity failure amounts to 100% if the liquid asset
liquid liability ratio equals -1, that it amounts to 100% if the liquid asset liquid liability ratio equals
0, that it amounts to 80% if the liquid asset liquid liability ratio equals 0.1, that it amounts to
40% if the liquid asset liquid liability ratio equals 0.2, that it amounts to 10% if the liquid asset
liquid liability ratio equals 0.3, that it amounts to 1% if the liquid asset liquid liability ratio equals
0.4, that it amounts to 0% if the liquid asset liquid liability ratio cquals 0.5, and that it amounts
to 0% if the liquid asset liquid liability ratio equals 1.
Suppose that the perceived likelihood of a solvency failure amounts to 100% if the total asset
total liability ratio equals 0, that it amounts to 100% if the total asset total liability ratio equals
0.8, that it amounts to 90% if the total asset total liability ratio cquals 0.9, that it amounts to
50% if the total asset total liability ratio equals 1, that it amounts to 10% if the total asset total
liability ratio equals 1.1, that it amounts to 0% if the total asset total liability ratio equals 1.2,
and that it amounts to 0% if the total asset total liability ratio equals 2.
The liquid asset liquid liability ratio is of course equal to the amount of liquid assets over the
amount of liquid deposits and loans. And the total asset total liability ratio equals the sum of
the fixed assets and the liquid assets over the sum of the liquid deposits and loans and the fixed
deposits and loans.
The central bank issues a bank failure declaration (forcing a bank into bankruptcy) if the liquid
asset liquid liability ratio falls below 0.05 or the total asset total liability ratio falls below 0.9.
1. ( /8) Make a System Dynamics simulation model of this
verify the model.
ue on your computer. Save and
2. ( /1) Simulate the model first of all over a time horizon of about 60 days without any anger
or an ‘organised’ bank run. In other words, set anger equal to 0, concerted liquid fraction
running away away equal 0%, and the credibility of the denials equal to 90%. Make graphs
of liquid deposits and loans lost and the perceived likelihood of a bank failure, both on your
computer and on this exam copy.
°Even without losing money (in case of depositor guarantees), depositors have to wait for months to get their
money back.
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Cas 27
3. ( /5) Now, adapt the model to simulate a bank run following Pieter Lakeman’s call for an
concerted bank run. Suppose for example that the concerted liquid fraction running away
jumps to 5% on day 2 and falls down to 0% on day 4 and that the credibility of the denials
falls from 90% to 10% from day 2 on. Suppose also that on top of these changes the variable
anger amounts to 0.5 and the liquidation premium to 25%. Save the model using your family
name, the number of the question, and the version.
(a) Simulate the model over a time horizon of 60 days. Make graphs of liquid deposits and
loans lost and the perceived likelihood of a bank failure, both on your computer and on
this exam copy.
(b) Explain the behaviours obtained, especially if you obtain strange behaviours.
(c) Briefly describe whether and what the bank could do to prevent this bank run (do not
model it here).
4. (/3) Simulate a bad
1, hindrance of bank failures
nario, again over a time horizon of 60 days, in which anger is
s 1, and the liquidation premium is 25%.
ic
(a) Make graphs of liquid deposits and loans lost and the perceived likelihood of a bank
failure, both on your computer and on this exam copy.
(b) Briefly describe the differences with the previous behaviour?
(c) Briefly describe whether and what the bank could do to prevent this bank run (do not
model it here).
s. List
5. (/1) Validate the model extremely briefly. Use maximum 2 (different) validation te
the tests used and briefly describe the conclusions of the tests.
6. ( /4) Draw a causal loop diagram of the system to help you communicate the main feedback
effects responsible for the bank run.
7. (/1) Explain the link between structure & behaviour briefly (e.g. for the ‘bad case’ scenario).
d loop policy (in colour)
est the policy at least
s on your exam copy.
8. ( /1) Save your model under another name and add a simple clos
that prevents the bank from collapsing. Describe the policy
in case of the ‘bad ¢ nario and sketch the resulting dynami
se
9. (/1) How do we call variables like hindrance of bank failures and anger?
D_ Chasing Rare Minerals/Metals?
Rare earth metals are necessary in ever bigger quantities for all sorts of innovative —mostly ‘green’-
technologie: colar cells, led lamps, mobile phones, et cetera. But
these metals s the name already suggests, rare. Moreover, some countries such as China,
which already have quasi-monopolies on the extraction of particular > metals, are said to
have constrained the export of these rare metals. These natural or artificial constraints ma
to temporary or/and structural scarcity, which in tum may hinder the transition of our s
towards a more sustainable one...
Make a SD model about the dynamics of the extraction and scarcity of a particular —non-
specified rare metal, ‘metal X’, based on the following description, and simulate it over the
period 2000 to 2050.
such a
hybrid cars, flat screen
are
lead
ciety
28
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Ca
D.1_ Extraction, Use and Recycling
Unextracted reserves of metal X, initially equal to 10000t, decrease through extraction with a
yearly extraction time of one ye ally equal to
the initial demand for metal X from 400t per year, and production of metal-X-containing products
decreases the supply of metal X stock after an average production time of metal-X-containing
products of a year. That increases the quantity of metal X in use, initially equal to 3000t.
After an average lifetime of metal X in use of 10 years, part of this quantity of metal X in use
cycled and the rest is lost. This division depends on the recycling fraction of metal X. Initially,
there is no metal X in recycling. The annual recycling time of metal X is one year and generates
a supply of recycled metal X flow which increases the supply of metal X stock, and determines
—together with the expected price driven demand for metal X~ the desired extraction of metal X.
. Extraction increases the supply of metal X, in
is ree
This desired extraction drives the extraction.
1. Make a preliminary System Dynamics simulation model of this issue. Use, if necessary,
first-order delay structures.
2. Make a detailed causal loop diagram of the stock-flow diagram above. How many feedback
loops are there?
D.2_ Intrinsic demand, price driven demand, recycling demand, etc.
Suppose that the expected intrinsic demand for metal X, initially equal to 400t (see above), in-
creases annually with an expected percentage increase of the intrinsic demand for metal X of 3%
per year. Model the expected price driven demand for metal X as a first-order delay of a year
—with initial value the expected initial demand for metal X— of the following fraction:
expected intrinsic demand for metalX
relative price metal X
The price effect supply shortage of metal X is a graph/lookup function with as argument:
expected price driven demand for metal X /production metal X containing products. The desired
recycling of metal X equals this expected price driven demand for metal X multiplied with the rel-
ative attractivity of recycling versus extraction plus the difference between the desired extraction
metal X and the real extraction of metal X.
The recycling fraction of metal X is equal to the fraction available of desired recycling of metal
X times the d recycling of metal X divided by the maximal recyclable quantity metal X.
The latter fre arily needs to be limited at a maximum of 1. The macimal recyclable
quantity of metal X equals the quantity of metal X in use which becomes available at the end of
the average lifetime of metal X in use of 10 years. Suppose that the fraction available of desired
recycling of metal X increases as follows: 10% in 2000, 50% in 2010, 80% in 2020, 89% in 2030,
90% in 2040 at which it stabilises. The effective fraction recycled supply of total supply metal X
equals the supply of recycled metal X divided by the sum of the extraction of metal X and the
supply of recycled metal X.
Suppose that the relative recycling cost of metal X decreases from 10 (so 10 times the normal
extraction cost) in 2000, to 2 in 2010, to 1 in 2020, to 0.9 in 2030 at which it stabilises, and that
the relative exploitation cost of metal X is a function of the fraction remaining reserves of metal
X with values (0, 100), (0.05, 2.5), (0.1, 1.25), (0.15, 1.1), (0.2, 1), (0.25, 1) (in other words, at
a fraction of 5% the relative cost is 2.5 times as high as with a fraction of 20% or more). The
average cost of metal X is then the weighted average of the relative recycling cost of metal X and
the relative exploitation cost van metal X, proportional to the fraction of recycled supply of total
supply of metal X. The fraction remai
of metal X divided by the initial reserves of metal X.
ing reserves of metal X is of course equal to the reserves
1
10This relative attractivity could be modelled as: " ‘
Talative caploitationcoat of metal X + Telative recyclingaoat metal X
Pruyt, 2010. Making System Dynamics Cool I: New Hot Teaching/Testing Ca 29
Suppose now that the market functions such that the relative price of metal X equals the
average cost of metal X times the ‘price effect supply shortage of metal X’. Suppose that this
price effect is a function of the demand/supply fraction, or here, of the expected price driven
demand for metal X divided by the production of metal X containing products, with values (0,
0.1), (1, 1), (1.5, 2), (2, 10), (5, 100) (in other words, a demand/supply fraction of 5 leads to a
100 times higher price than usual).
Also make sure that there is not more extraction than there are non-extracted resources. And
add an output indicator to monitor the fraction delivered of the intrinsic demand of metal X. This
equals the supply of metal X divided by the expected intrinsic demand for metal X.
1. Extend the simulation model with the information above. Verify the model briefly.
Simulate the model and make graphs of the expected price driven demand for metal X, the
relative price of metal X, the reserves of metal X, and the output indicator fraction supplied
of intrinsic demand for metal X.
2. Validate the model. List 2 validation tests, perform them and describe the results (briefly).
3. Test the sensitivity of the model (more specifically the fraction delivered of intrinsic demand
for metal X and the reserves of metal X) for (small) changes in following functions and
parameters: the price effect supply shortage of metal X, the initial reserves of metal X, and
the fraction available of desired recycling of metal X. Describe briefly the tests you performed,
and your results and conclusions.
4. Make an extremely aggregated causal loop diagram of the model which allows you to explain
the main feedback loop effects.
5. Explain the link between system and behaviour (more specifically of the output indicator).
D.2.1 Strategic and speculative reserves (BONUS)
When it comes to scarcity of metals, people are scared that strategic and speculative reserves are
built, especially by states that already have a quasi-monopoly on the exploitation.
1. Extend the model with a submodel dealing with strategic reserves (for national use, which
means they are not available on the world market). Simulate the model and sketch the
difference in behaviour.
2. Extend the model with a submodel dealing with speculative reserves (temporarily unavailable
on the market to be sold later for a higher price on the market). Simulate the model and
sketch the difference in behaviour.
