Ebook: Differential Equations Models in Biology, Epidemiology and Ecology: Proceedings of a Conference held in Claremont California, January 13–16, 1990

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.

---

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.

---

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.
Content:
Front Matter....Pages N2-5
Front Matter....Pages 7-7
The Problem of Relevant Detail....Pages 9-15
Lifespans in Population Models: Using Time Delays....Pages 16-27
Convergence to Equilibria in General Models of Unilingual-Bilingual Interactions....Pages 28-33
The Sherman-Rinzel-Keizer Model for Bursting Electrical Activity in the Pancreatic ?-Cell....Pages 34-53
Front Matter....Pages 55-55
Models for the Spread of Universally Fatal Diseases II....Pages 57-69
Nonexistence of Periodic Solutions for a Class of Epidemiological Models....Pages 70-79
On the Solution of the Two-Sex Mixing Problem....Pages 80-98
Modelling the Effects of Screening in HIV Transmission Dynamics....Pages 99-120
An S?E?I Epidemic Model with Varying Population Size....Pages 121-138
Stability Change of the Endemic Equilibrium in Age-Structured Models for the Spread of S—I—R Type Infectious Diseases....Pages 139-158
Front Matter....Pages 159-159
Mathematical Model for the Dynamics of a Phytoplankton Population....Pages 161-176
Some Delay Models for Juvenile vs. Adult Competition....Pages 177-188
McKendrick Von Foerster Models for Patch Dynamics....Pages 189-199
Generic Failure of Persistence and Equilibrium Coexistence in a Model of m-species Competition in an n-vessel Gradostat when m > n ....Pages 200-209
Boundedness of Solutions in Neutral Delay Predator-Prey and Competition Systems....Pages 210-218
Some Examples of Nonstationary Populations of Constant Size....Pages 219-234
Coexistence in Competition-Diffusion Systems....Pages 235-246
Population Interactions with Growth Rates Dependent on Weighted Densities....Pages 247-256
Global Stability in a Population Model with Dispersal and Stage Structure....Pages 257-267
Erratum....Pages 269-269
Back Matter....Pages 271-273

---

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.
Content:
Front Matter....Pages N2-5
Front Matter....Pages 7-7
The Problem of Relevant Detail....Pages 9-15
Lifespans in Population Models: Using Time Delays....Pages 16-27
Convergence to Equilibria in General Models of Unilingual-Bilingual Interactions....Pages 28-33
The Sherman-Rinzel-Keizer Model for Bursting Electrical Activity in the Pancreatic ?-Cell....Pages 34-53
Front Matter....Pages 55-55
Models for the Spread of Universally Fatal Diseases II....Pages 57-69
Nonexistence of Periodic Solutions for a Class of Epidemiological Models....Pages 70-79
On the Solution of the Two-Sex Mixing Problem....Pages 80-98
Modelling the Effects of Screening in HIV Transmission Dynamics....Pages 99-120
An S?E?I Epidemic Model with Varying Population Size....Pages 121-138
Stability Change of the Endemic Equilibrium in Age-Structured Models for the Spread of S—I—R Type Infectious Diseases....Pages 139-158
Front Matter....Pages 159-159
Mathematical Model for the Dynamics of a Phytoplankton Population....Pages 161-176
Some Delay Models for Juvenile vs. Adult Competition....Pages 177-188
McKendrick Von Foerster Models for Patch Dynamics....Pages 189-199
Generic Failure of Persistence and Equilibrium Coexistence in a Model of m-species Competition in an n-vessel Gradostat when m > n ....Pages 200-209
Boundedness of Solutions in Neutral Delay Predator-Prey and Competition Systems....Pages 210-218
Some Examples of Nonstationary Populations of Constant Size....Pages 219-234
Coexistence in Competition-Diffusion Systems....Pages 235-246
Population Interactions with Growth Rates Dependent on Weighted Densities....Pages 247-256
Global Stability in a Population Model with Dispersal and Stage Structure....Pages 257-267
Erratum....Pages 269-269
Back Matter....Pages 271-273
....