Epidemic Module Description

Understanding Disease and Epidemics (Team 21, Portland, Oregon)

The Portland (Team 21) module will focus on diseases and epidemics. It will include activities appropriate for mathematics classes at several levels, biology classes, health classes, history/social science classes, and environmental science classes. All sequences of activities will have some common elements. Each will begin with a simulation activity developed by Will Glass-Hussain while he was a graduate student at MIT known as the Epidemic or Nerd (New England Regional Disease) Game. In this simulation a disease is transmitted through a class by a handshake. The debriefing of this activity leads naturally into the development of a formal model. We will develop appropriate models for this simulation and other activities in a variety of software packages. All models will be developed in both STELLA and Excel. The simpler models will also be developed in Mathematica and Maple. Activities will include options in which students actually build the models and options in which students use pre-built models. (A sequence of models and the software used is included with this proposal).

Past use of the basic infection/disease model has shown that the most common student criticism of the model has been the fact that the model does not include recovery from the disease. The SIR model (Susceptible->Infected->Recovered) model addresses this issue. It not only presents a more realistic picture of disease spread, but also allows exploration of what factors control the development of a disease into an epidemic. It is anticipated that student activities will focus around understanding what allows epidemics to occur. Further, the mathematics activities will include actual development of a mathematical expression for the criteria for epidemic development.

Exploration of the SIR model will include the role of vaccination in controlling disease and the role of natural immunity in preventing epidemics. Activities for all disciplines will include some exploration of historical scenarios (largely drawn from William McNeill's Plagues and People and the work done by Jeff Potash and John Heinbokel of the Center for System Dynamics at the Vermont Common School). An optional extension will include use of conveyors instead of standard stocks.

The SIR model will provide the core model for further development. This will involve looking at diseases in which there is a non-symptomatic and non-contagious phase. This model will also be explored in conjunction with varying vaccination and natural immunity. The next extension will look at "virgin soil" scenarios in which lack of immunity in the affected population results in a higher mortality due to secondary effects. This will require development of a "mortality" option in the recovery process for the basic SIR model.

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