Explorations in Computational Science: Hands-on Computational Modeling using STELLA

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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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Session Goals

• 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

• 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

• 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!)

• 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?

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Mathematical Basis of STELLA (an intro to ODE's!)
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STELLA Implementation
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STELLA Basic Elements

• 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

• 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

• Goal create a computational model of the
  boarding school epidemic
• Algorithm 1927 Kermack-McKendrick SIR algorithm
• Three types of students
• Susceptibles
• Infecteds
• Recovereds

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Case Study Influenza Epidemic

• 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