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An introduction ISBN 9780387953540
Description
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.
Table of Contents
New directions in the mathematics of infectious disease * Fred Brauer * Kenneth L. Cooke * 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
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Models, methods, and theory ISBN 9780387953557
Description
This IMA Volume in Mathematics and its Applications MATHEMATICAL APPROACHES FOR EMERGING AND REEMERGING INFECTIOUS DISEASES: MODELS, AND THEORY METHODS is based on the proceedings of a successful one week workshop. The pro ceedings of the two-day tutorial which preceded the workshop "Introduction to Epidemiology and Immunology" appears as IMA Volume 125: Math ematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction. The tutorial and the workshop are integral parts of the September 1998 to June 1999 IMA program on "MATHEMATICS IN BI OLOGY. " I would like to thank Carlos Castillo-Chavez (Director of the Math ematical and Theoretical Biology Institute and a member of the Depart ments of Biometrics, Statistics and Theoretical and Applied Mechanics, Cornell University), Sally M. Blower (Biomathematics, UCLA School of Medicine), Pauline van den Driessche (Mathematics and Statistics, Uni versity of Victoria), and Denise Kirschner (Microbiology and Immunology, University of Michigan Medical School) for their superb roles as organizers of the meetings and editors of the proceedings. Carlos Castillo-Chavez, es pecially, made a major contribution by spearheading the editing process. I am also grateful to Kenneth L. Cooke (Mathematics, Pomona College), for being one of the workshop organizers and to Abdul-Aziz Yakubu (Mathe matics, Howard University) for serving as co-editor of the proceedings. I thank Simon A. Levin (Ecology and Evolutionary Biology, Princeton Uni versity) for providing an introduction.
Table of Contents
New directions in the mathematics of infectious diseases * Fred Brauer * Kenneth Cooke * Maximal prevalence and the basic reproduction number in simple epidemics * The transition through stages with arbitrary length distributions, and applications in epidemics * Measles outbreaks are not chaotic * Epidemics among a population of households * Infection transmission dynamics and vaccination program effectiveness as a function of vaccine effects in individuals * The influence of different forms of cross-protective immunity on the population dynamics of antigenetically diverse pathogens * Dynamics of multiple strains of infectious agents coupled by cross-immunity * Virulence evolution in macro-parasites * Mathematical models for schistosomiasis with delays and multiple definitive hosts * Infectious disease models with chronological age structure and epidemiological age structure * Effects of genetic heterogeneity on HIV transmission in homosexual populations * Age-structured core group model and its impact on STD dynamics * Global dynamics of tuberculosis models with density dependent demography * Global stability in some SEIR epidemic models * The global stability analysis for an SIS model with age and infection age structures * Endemic threshold and stability in an evolutionary epidemic model * Epilogue
by "Nielsen BookData"
