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Mathematical Theories of Populations: Deomgraphics, Genetics, and EpidemicsMathematical Theories of Populations: Deomgraphics, Genetics, and Epidemics

Frank Hoppensteadt



CBMS-NSF Regional Conference Series in Applied Mathematics 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.

Contents

The Equations of Population Dynamics: Age Dependent Population Growth; Analysis of the Birth Rate; A Model of a Self-Limiting Population; A Two-sex Model; Deterministic Models in Genetics: A Brief Introduction to Mendelian Genetics; The One-Locus, two-allele Model; Age Dependent Population Genetics. Propagation of a Gene in a Spatially Distributed Population; Theories of Epidemics: General Theory of Contagious Phenomena; Qualitative Behavior of Deterministic Epidemics.

1975 / vii + 72 pages / Softcover / ISBN-13: 978-0-898710-17-5 / ISBN-10: 0-89871-017-0 /
List Price $40.50 / SIAM/CBMS Member Price $28.35 / Order Code CB20
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