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Explorations in Computational Science:
Hands-on Computational Modeling using STELLA
Presenter:
Robert R. Gotwals (“Bob2”)
Shodor Education Foundation, Inc.
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National Computational Science Leadership Program (NCSLP)
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Session Goals
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First experience in computational science
» Application: computational epidemiology
» Algorithm: 1927 Kermack-McKendrick SIR algorithm
First experience with an Architecture: STELLA on a PC
» computational tool
– STELLA
Logistics
» Short overview
» Hands-on model building exercise
» Extensions as time permits
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System Dynamics
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A method of studying dynamic (time-driven) phenomena through the
use of:
» Computer simulations based on ordinary differential equations
» Development of causal mechanisms (feedback loops)
» Analysis of the factors that affect a system (a collection of
interacting elements)
Examples:
» Interactions of predators and prey in an ecosystem
» Fate, transport, and distribution of a pharmaceutical through a
patient
» Photooxidation of precursor atmospheric pollutants becoming
ozone
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STELLA Highlights
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no programming skills required
Relatively short learning-curve
icon-based: modelers need to understand functions of icons
graphs and tables easily constructed, manipulated, exported
mathematical engine underlying software fairly robust
mathematics is transparent to users
“authoring” capabilities, provides user-friendly graphical
interface to underlying models
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Mathematical Basis of STELLA (an
intro to ODE's!)
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we wish to be able to study events as they change over time.
main question: how do different elements change the event
over time?
Example: how does one's height change over time?
² height
² time
= some mathematical equation ( or function)
Suppose the height of an animal increases by 20% every year until it
is 20 years old?
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Mathematical Basis of STELLA (an
intro to ODE's!)
²h
²t
=
0.2h
or
dh = 0.2h
dt
Do some algebraic rearrangements:
dh = 0.2 h dt
then "integrate" both sides from starting time to stopping time:
t20
 dh 0.2hdt
where h at start equals 1 inch
t 0
h = e 0.2h * (20 - 0) (by definitions from integral calculus) = 54.6 inches
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STELLA Implementation
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STELLA Basic Elements
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Stocks
» act as "accumulators", have an initial
value
» viewed as having some unit
» are the "nouns" (things) for the system
Flows
» provide input/output to the stock
» have value of unit/time (unit same as
stock unit)
» are the "verbs" for the system
Converters
» hold constants or change units
» can be algebraic or graphical
» are the "adverbs" or "adjectives"
Connectors
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Case Study: Simple Epidemiology Model:
Influenza Epidemic in a Boarding School
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Source: Mathematical Biology, J.D. Murray, Springer-Verlag,
1989.
Background:
» In 1978, a study was conducted and reported in the British
Medical Journal (4 March 1978) of an outbreak of the
influenza virus in a boys boarding school. The school had a
population of 763 boys. Of these 512 were confined to bed
during the epidemic, which lasted from 22 January until 4
February. It seems that one infected boy initiated the
epidemic. At the outbreak of the epidemic, none of the boys
had previously had influenza, so no resistance to the
infection was present.
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Case Study: Influenza Epidemic
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Goal: create a
computational model of
the boarding school
epidemic
Algorithm: 1927
Kermack-McKendrick
SIR algorithm
Three “types” of
students:
» Susceptibles
» Infecteds
» Recovereds
dS
 rSI
dt
dI
rSIaI
dt
dR
aI
dt
where:
S= population of susceptible people
I = population of infected people
R = population of recovered people
r = probability of becoming infected
a = infectious period
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Case Study: Influenza Epidemic
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Extensions:
» What is the effect of vaccinations? Add a vaccination
algorithm. Use sensitivity analysis to analyze effect
» What is the effect of a return to susceptibility? Add a
return loop to susceptibility
» Add possibility of deaths, both as a result of disease and
natural deaths
» Add possibility of influx of new susceptibles
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