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This book grew out of the discussions and presentations that began during the Workshop on Emerging and Reemerging Diseases (May 17-21, 1999) sponsored by the Institute for Mathematics and its Application (IMA) at the University of Minnesota with the support of NIH and NSF. The workshop started with a two-day tutorial session directed at ecologists, epidemiologists, immunologists, mathematicians, and scientists interested in the study of disease dynamics. The core of this first volume, Volume 125, covers tutorial and research contributions on the use of dynamical systems (deterministic discrete, delay, PDEs, and ODEs models) and stochastic models in disease dynamics. The volume includes the study of cancer, HIV, pertussis, and tuberculosis. Beginning graduate students in applied mathematics, scientists in the natural, social, or health sciences or mathematicians who want to enter the fields of mathematical and theoretical epidemiology will find this book useful.
From the contents: New directions in the mathematics of infectious disease.- Fred Brauer: The man and his mathematics.- Kenneth L. Cooke: Researcher, educator par excellance.- Basic ideas of mathematical epidemiology.- Extensions of the basic models.- New vaccination strategies for pertussis.- Time delay in epidemic models.- Nonlocal response in a simple epidemiological model.- Discrete-time S-I-S models with simple and complex population dynamics.- Intraspecific competition, dispersal, and disease dynamics in discrete-time patchy environments.- The impact of long-range dispersal on the rate of spread in population and epidemic models.- Endemicity, persistence, and quasi-stationarity.- On the computation of Ro and its role in global stability.- Nonlinear mating models for populations with discrete generations.- Center manifolds and normal forms in epidemic models.- Remarks on modeling host-viral dynamics and treatment.- A multiple compartment model for the evolution of HIV-1 after highly active antiretroviral therapy.- Modeling cancer as an infectious disease.- Frequency dependent risk of infection and the spread of infectious diseases.- Long-term dynamics and emergence of tuberculosis.
From the reviews: "This two-volume set is based on a week-long workshop sponsored by the Institute of Mathematics and its Applications (the IMA) and held at the University of Minnesota in May 1999. ! There is a lot of valuable work in this two-volume set which could meet the intended aim of introducing people to research-level mathematical epidemiology." (Geoff Aldis, UK Nonlinear News, November 2002)