Differential Equations Models in Biology, Epidemiology and Ecology

1. Front Matter

   Pages N2-5

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2. Mathematical Biology

   1. Front Matter

      Pages 7-7

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   2. The Problem of Relevant Detail

      • Simon Levin

      Pages 9-15

   3. Lifespans in Population Models: Using Time Delays

      • Jacques Bélair

      Pages 16-27

   4. Convergence to Equilibria in General Models of Unilingual-Bilingual Interactions

      • H. I. Freedman, I. Baggs

      Pages 28-33

   5. The Sherman-Rinzel-Keizer Model for Bursting Electrical Activity in the Pancreatic β-Cell

      • Mark Pernarowski, Robert M. Miura, J. Kevorkian

      Pages 34-53

3. Epidemiology

   1. Front Matter

      Pages 55-55

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   2. Models for the Spread of Universally Fatal Diseases II

      • Fred Brauer

      Pages 57-69

   3. Nonexistence of Periodic Solutions for a Class of Epidemiological Models

      • Stavros Busenberg, P. van den Driessche

      Pages 70-79

   4. On the Solution of the Two-Sex Mixing Problem

      • C. Castillo-Chavez, S. Busenberg

      Pages 80-98

   5. Modelling the Effects of Screening in HIV Transmission Dynamics

      • Ying-Hen Hsieh

      Pages 99-120

   6. An S→E→I Epidemic Model with Varying Population Size

      • Andrea Pugliese

      Pages 121-138

   7. Stability Change of the Endemic Equilibrium in Age-Structured Models for the Spread of S—I—R Type Infectious Diseases

      • Horst R. Thieme

      Pages 139-158

4. Ecology and Population Dynamics

   1. Front Matter

      Pages 159-159

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   2. Mathematical Model for the Dynamics of a Phytoplankton Population

      • E. Beretta, A. Fasano

      Pages 161-176

   3. Some Delay Models for Juvenile vs. Adult Competition

      • J. M. Cushing

      Pages 177-188

   4. McKendrick Von Foerster Models for Patch Dynamics

      • Alan Hastings

      Pages 189-199

   5. Generic Failure of Persistence and Equilibrium Coexistence in a Model of m-species Competition in an n-vessel Gradostat when m > n

      • Willi Jäger, Hal Smith, Betty Tang

      Pages 200-209

   6. Boundedness of Solutions in Neutral Delay Predator-Prey and Competition Systems

      • Y. Kuang

      Pages 210-218

   7. Some Examples of Nonstationary Populations of Constant Size

      • Fabio A. Milner, Tanya Kostova

      Pages 219-234

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.

• Ecology
• Mathematical Biology
• Population Dynamics
• differential equation
• epidemiological
• epidemiology
• plankton

• Department of Mathematics, Harvey Mudd College, Claremont, USA

  Stavros Busenberg

• Department of Mathematics, California State University, Fullerton, USA

  Mario Martelli

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