This volume is intended for mathematicians, statisticians, biologists, and medical researchers who are interested in recent advances in analyzing changes in populations of genes, cells, and tumors; in the natural history of cancer; and in epidemiological topics such as AIDS.
The selection of subjects was motivated by recent developments in the mathematical theory of populations and by new data available from various branches of molecular and cellular biology and biomedical sciences. The topics included have been selected from those presented at the Second International Conference on Mathematical Population Dynamics. No attempt has been made to cover all of the traditional topics in population biology. The chapters are grouped within the following topics: structured populations, ordinary and partial differential equations models, AIDS and theory of epidemics, stochastic models, cell cycle kinetics, proliferation and tumor growth, and genetics and molecular biology.
This volume appears at a time when there are important developments occurring in mathematics and biology. From the mathematical viewpoint, there has been recent progress in models of structured populations. These arc models that identify variables such as age, size, amounts of specific constituents, or other characteristics of individuals (genes, cells, or organisms) to reproduce the time evolution of heterogeneity within populations. On the most abstract level, these new models require analysis of integral, functional, and partial differential equations (frequently achieved by the analysis of semigroups of operators) replacing the traditional ordinary differential equation formalism. There also has been recent progress in stochastic models involving a discrete or continuous variety of types of individuals within a population...