Mathematical Theories of Populations: Demographics, Genetics, and Epidemics (CBMS-NSF Regional Conference Series in Applied Mathematics, Series Number 20)

Mathematical theories of populations have appeared both implicitly and explicitly in many important studies of populations, human populations as well as populations of animals, cells and viruses. They provide a systematic way for studying a population's underlying structure. A basic model in population age structure is studied and then applied, extended and modified, to several population phenomena such as stable age distributions, self-limiting effects, and two-sex populations. Population genetics are studied with special attention to derivation and analysis of a model for a one-locus, two-allele trait in a large randomly mating population. The dynamics of contagious phenomena in a population are studied in the context of epidemic diseases. Mathematical Theories of Populations: Demographics, Genetics and Epidemics......Page 3 ISBN 0-89871-017-0......Page 6 Contents......Page 7 Preface......Page 9 1. Age dependent population growth......Page 13 2. Analysis of the birth rate: stable age distribution......Page 18 3. A model of a self-limiting population.......Page 21 4. A two-sex model......Page 23 Bibliography......Page 26 1. A brief introduction to Mendelian genetics......Page 29 2. The one-locus, two-allele model......Page 31 3. Age dependent population genetics......Page 44 4. Propagation of a gene in a spatially distributed population......Page 48 Bibliography......Page 55 1. General theory of contagious phenomena......Page 57 2. Qualitative behavior of deterministic epidemics......Page 66 Bibliography......Page 83