Mathematical Approaches For Emerging And Reemerging Infectious Diseases: Models, Methods, And Theory (the Ima Volumes In Mathematics And Its Applications)

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. Front Matter....Pages i-x New Directions in the Mathematics of Infectious Disease....Pages 1-5 Fred Brauer: The Man and His Mathematics....Pages 7-20 Kenneth L. Cooke: Researcher, Educator Par Excellence....Pages 21-30 Maximal Prevalence and the Basic Reproduction Number in Simple Epidemics....Pages 31-44 The Transition Through Stages with Arbitrary Length Distributions, and Applications in Epidemics....Pages 45-84 Measles Outbreaks are not Chaotic....Pages 85-114 Epidemics Among a Population of Households....Pages 115-142 Infection Transmission Dynamics and Vaccination Program Effectiveness as a Function of Vaccine Effects in Individuals....Pages 143-155 The Influence of Different Forms of Cross-Protective Immunity on the Population Dynamics of Antigenically Diverse Pathogens....Pages 157-169 Dynamics of Multiple Strains of Infectious Agents Coupled by Cross-Immunity: A Comparison of Models....Pages 171-191 Virulence Evolution in Macro-Parasites....Pages 193-213 Mathematical Models for Schistosomiasis with Delays and Multiple Definitive Hosts....Pages 215-229 Infectious Disease Models with Chronological Age Structure and Epidemiological Age Structure....Pages 231-243 Effects of Genetic Heterogeneity on HIV Transmission in Homosexual Populations....Pages 245-260 Age-Structured Core Group Model and its Impact on STD Dynamics....Pages 261-273 Global Dynamics of Tuberculosis Models with Density Dependent Demography....Pages 275-294 Global Stability in Some Seir Epidemic Models....Pages 295-311 The Global Stability Analysis for an SIS Model with Age and Infection Age Structures....Pages 313-335 Endemic Threshold and Stability in an Evolutionary Epidemic Model....Pages 337-359 Back Matter....Pages 361-377 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 proƯ ceedings of the two-day tutorial which preceded the workshop "Introduction to Epidemiology and Immunology" appears as IMA Volume 125: MathƯ 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 BIƯ OLOGY." I would like to thank Carlos Castillo-Chavez (Director of the MathƯ ematical and Theoretical Biology Institute and a member of the DepartƯ 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, UniƯ 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, esƯ 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 (MatheƯ matics, Howard University) for serving as co-editor of the proceedings. I thank Simon A. Levin (Ecology and Evolutionary Biology, Princeton UniƯ versity) for providing an introduction 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 to ecologists, epidemiologists, immunologists, mathematicians, and scientists interested in the study of disease dynamics. The core of this second volume, Volume 126, covers research contributions on the use of dynamical systems (deterministic discrete, delay, PDEs, and ODEs models) and stochastic models in disease dynamics. Contributions motivated by the study of diseases like influenza, HIV, tuberculosis, and macroparasitic like schistosomiasis are also included. This second volume requires additional mathematical sophistication, and graduate students in applied mathematics, scientists in the natural, social, and health sciences, or mathematicians who want to enter the field of mathematical and theoretical epidemiology will find it useful. The collection of contributors includes many who have been in the forefront of the development of the subject. 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 second volume, Volume 126, covers research contributions on the use of dynamical systems (deterministic discrete, delay, PDEs, and ODEs models) and stochastic models in disease dynamics. Contributions motivated by the study of diseases like influenza, HIV, tuberculosis, and macroparasitic like schistosomiasis are also included. This second volume requires additional mathematical sophistication, and graduate students in applied mathematics, scientists in the natural, social, and health sciences, or mathematicians who want to enter the field of mathematical and theoretical epidemiology will find it useful. The collection of contributors includes many who have been in the forefront of the development of the subject.

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 to 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.