Georgia Institute of Technology College of Sciences

After some brief comments about the nature of mathematical modeling in biology and medicine, we will formulate and analyze the SIR infectious disease transmission model. The model is a system of three non-linear differential equations that does not admit a closed form solution. However, we can apply methods of dynamical systems to understand a great deal about the nature of solutions. Along the way we will use this model to develop a theoretical foundation for public health interventions, and we will observe how the model yields several fundamental insights (e.g., threshold for infection, herd immunity, etc.) that could not be obtained any other way. At the end of the talk we will compare the model predictions with data from actual outbreaks.