The past forty years have been the stage for the maturation of mathematical biolo~ as a scientific field. The foundations laid by the pioneers of the field during the first half of this century have been combined with advances in ap plied mathematics and the computational sciences to create a vibrant area of scientific research with established research journals, professional societies, deep subspecialty areas, and graduate education programs. Mathematical biology is by its very nature cross-disciplinary, and research papers appear in mathemat ics, biology and other scientific journals, as well as in the specialty journals devoted to mathematical and theoretical biology. Multiple author papers are common, and so are collaborations between individuals who have academic bases in different traditional departments. Those who seek to keep abreast of current trends and problems need to interact with research workers from a much broader spectrum of fields than is common in the traditional mono-culture disciplines. Consequently, it is beneficial to have occasions which bring together significant numbers of workers in this field in a forum that encourages the exchange of ideas and which leads to a timely publication of the work that is presented. Such an occasion occurred during January 13 to 16, 1990 when almost two hun dred research workers participated in an international conference on Differential Equations and Applications to Biology and Population Dynamics which was held in Claremont.

Klappentext

The meeting explored current directions of research in population problems, epidemiology and ecology and celebrated the contributions of Kenneth Cooke to this field on the occasion of his 65th birthday. The volume contains a keynote paper by Simon Levin where he raises and discusses the question of how much detail is relevant in a variety of efforts to model and analyze biological phenomena. The research contributions which form the bulk of the volume are collected in three sections titled: Mathematical Biology, Epidemiology and Ecology and Population Dynamics. These articles contain original results which individually extend their particular research topics. In each of the sections, the collection of expert contributions serve to delineate current research frontiers and point out the major modern research trends of the field. A companion volume in the mathematics series (LN in Mathematics, Vol. 1475) contains contributions on delay differential equations and related dynamical systems.

Inhalt
Mathematical Biology.- The Problem of Relevant Detail.- Lifespans in Population Models: Using Time Delays.- Convergence to Equilibria in General Models of Unilingual-Bilingual Interactions.- The Sherman-Rinzel-Keizer Model for Bursting Electrical Activity in the Pancreatic ??-Cell.- Epidemiology.- Models for the Spread of Universally Fatal Diseases II.- Nonexistence of Periodic Solutions for a Class of Epidemiological Models.- On the Solution of the Two-Sex Mixing Problem.- Modelling the Effects of Screening in HIV Transmission Dynamics.- An S?E?I Epidemic Model with Varying Population Size.- Stability Change of the Endemic Equilibrium in Age-Structured Models for the Spread of S-I-R Type Infectious Diseases.- Ecology and Population Dynamics.- A Mathematical Model for the Dynamics of a Phytoplankton Population.- Some Delay Models for Juvenile vs. Adult Competition.- McKendrick Von Foerster Models for Patch Dynamics.- Generic Failure of Persistence and Equilibrium Coexistence in a Model of m-species Competition in an n-vessel Gradostat when m > n.- Boundedness of Solutions in Neutral Delay Predator-Prey and Competition Systems.- Some Examples of Nonstationary Populations of Constant Size.- Coexistence in Competition-Diffusion Systems.- Population Interactions with Growth Rates Dependent on Weighted Densities.- Global Stability in a Population Model with Dispersal and Stage Structure.