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Thursday, February 05, 2009
3:30 PM - 3:30 PM
CNLS Conference Room (TA-3, Bldg 1690)


Converting PDE age-of-infection models into ODEs

Joel Miller

Much of the mathematical theory of infectious disease spread is based on the assumptions of uniform mixing, constant infectiousness, and exponentially distributed infection duration. These assumptions allow us to write down ODE models for the spread of an epidemic. Unfortunately, the underlying assumptions are invalid. The failure of uniform mixing has been studied considerably in network model. However, infectiousness varies as an individual progresses through the infectious period, and the duration of infection is frequently peaked around a typical time scale. The approaches to investigate the age-of-infection models have relied on PDE models. In this talk we will focus on how to accommodate age-of-infection models into a simple ODE model. This is work in progress. This talk will be fairly informal and hopefully have a number of interruptions.