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

1. Explorations in Computational Science: Hands-on Computational Modeling using STELLA Presenter: Robert R. Gotwals (“Bob2”) Shodor Education Foundation, Inc.

2. 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

3. 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

4. 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

5. 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?

6. Mathematical Basis of STELLA (an intro to ODE's!)

7. STELLA Implementation

8. 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

9. 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.

10. 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

11. 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