Mathematical Theories of Populations

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 populations 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.

Spis treści:
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.