Chapter 1

Mathematical Approaches to Infectious Disease Prediction and Control

Nedialko B. Dimitrov
Operations Research Department, Naval Postgraduate School, Monterey, California 93943, ned@alumni.cs.utexas.edu

Lauren Ancel Meyers
Section of Integrative Biology, The University of Texas at Austin, Austin,Texas 78712, and Santa Fe Institute, Santa Fe, New Mexico 87501, laurenmeyers@mail.utexas.edu

Abstract
Mathematics has long been an important tool for understanding and controlling the spread of infectious diseases. Here, we begin with an overview of compartmental models, the traditional approach to modeling infectious disease dynamics, and then introduce contact network epidemiology, a relatively new approach that applies bond percolation on random graphs to model the spread of infectious disease through heterogeneous populations. As we illustrate, these methods can be used to address public health challenges and have recently been coupled with powerful computational methods to optimize epidemic control strategies.

Key words: infectious disease modeling; infectious disease control; analytical modeling; network analysis

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Citation information:

Dimitrov, N. B., L. A. Meyers. 2010. Mathematical approaches to infectious disease prediction and control. J. J. Hasenbein, ed. INFORMS TutORials in Operations Research, Vol. 7. INFORMS, Hanover, MD, pp. 1--25.