Carlos Castillo-Chavez, Arizona State University

Friday, August 3, 1:00 p.m. - 1:50 p.m., Ballroom A

The concept of threshold or tipping point, a mathematical dimensionless quantity that characterizes the conditions required for the occurrence of a drastic transition between states, is central to the study of the transmission dynamics and control of diseases such as dengue, influenza, SARS, malaria, and tuberculosis, to name a few. The quantification of tipping point phenomena goes back to the modeling and mathematical work of Sir Ronald Ross (second Nobel laureate in medicine, 1911;) and his "students" (Kermack and McKendrick, 1927, 1932). Ross, in fact, proceeded to confront the challenges associated with understanding and managing malaria patterns at the population level right after the completion of his scientific malaria discoveries. The quantification of the concept of tipping point, in the context of epidemiology, has found countless applications directly tied in to the design, development, and implementation of public health policy. Ross's writings emphasized the value of mathematical models as integrators of multilevel information and processes, and his mathematical framework led to the development of a mathematical theory of infectious diseases (an outstanding review of the field can be found in Hethcote, SIAM Review, 2000). The overview in this lecture provides a personal perspective on the role of mathematical models in the study of the dynamics, evolution, and control of infectious diseases over multiple scales.