Biological Growth and Spread

1. Front Matter

   Pages I-XI

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2. Proliferation, spread and reaction-dispersal processes

   1. Front Matter

      Pages 1-2

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   2. Biological Aspects

      1. Genetic Basis of Biological Growth

         • Renato Baserga

         Pages 3-8

      2. Some Observations on the Kinetics of Haehomoietic Stem Cells and their Relationship to the Spatial Cellular Organisation of the Tissue

         • B. I. Lord, R. Schofield

         Pages 9-22

      3. Proliferative Cell Populations in Surface Epithelia: Biological Models for Cell Replacement

         • C. S. Potten

         Pages 23-35

   3. Mathematical Aspects and Applications

      1. Density dependent Markov population processes

         • A. D. Barbour

         Pages 36-49

      2. A Model of Development of a Cell

         • R. Bartoszyński

         Pages 50-56

      3. Spatial Spread in Branching Processes

         • J. D. Biggins

         Pages 57-67

      4. Pattern Formation by Bacteria

         • F. C. Hoppensteadt, W. Jäger

         Pages 68-81

      5. Random processes in random environments

         • Harry Kesten

         Pages 82-92

      6. Segregation Model and its Applications

         • Masao Nagasawa

         Pages 93-97

      7. Positive Recurrence of Multi-Dimensional Population-Dependent Branching Processes

         • W. Rittgen

         Pages 98-108

      8. Population Growth with Large Random Fluctuations

         • Henry C. Tuckwell

         Pages 109-118

      9. Niche Overlap and Invasion of Competitors in Random Environments II. The Effects of Demographic Stochasticity

         • Michael Turelli

         Pages 119-129

      10. Behavior of Limiting Diffusions for Density-Dependent Branching processes

          • Carla Wofsy

          Pages 130-137

3. Random systems with locally interacting objects

   1. Front Matter

      Pages 139-139

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   2. Theory

      1. Local Interactions with a Global Signal: A Voter Model

         • H. Föllmer

         Pages 141-144

      2. Interacting Markov Processes

         • Thomas M. Liggett

         Pages 145-156

      3. On a Class of Branching Processes on a Lattice with Interactions

         • Klaus Schürger

         Pages 157-164

   3. Models

      1. The Asymptotic Behavior of a Probabilistic Model for Tumor Growth

         • Maury Bramson, David Griffeath

         Pages 166-172

These Proceedings have been assembled from papers presented at the Conference on Models of Biological Growth and Spread, held at the German Cancer Research Centre Heidelberg and at the Institute of Applied Mathematics of the University of Heidelberg, July 16-21, 1979. The main theme of the conference was the mathematical representation of biolog­ ical populations with an underlying spatial structure. An important feature of such populations is that they and/or their individual com­ ponents may interact with each other. Such interactions may be due to external disturbances, internal regulatory factors or a combination of both. Many biological phenomena and processes including embryogenesis, cell growth, chemotaxis, cell adhesion, carcinogenesis, and the spread of an epidemic or of an advantageous gene can be studied in this con­ text. Thus, problems of particular importance in medicine (human and veterinary), agriculture, ecology, etc. may be taken into consideration and a deeper insight gained by utilizing (more) realistic mathematical models. Since the intrinsic biological mechanisms may differ considerably from each other, a great variety of mathematical approaches, theories and techniques is required. The aims of the conference were (i) To provide an overview of the most important biological aspects. (ii) To survey and analyse possible stochastic and deterministic approaches. (iii) To encourage new research by bringing together mathematicians interested in problems of a biological nature and scientists actively engaged in developing mathematical models in biology.

• Biologisch-mathematisches Modell
• bacteria
• biology
• cancer
• cancer research
• cell
• epidemiology
• gene
• genetics
• kinetics
• mathematics
• migration
• population genetics
• stem cells
• tissue

• Institut für Angewandte Mathematik, Universität Heidelberg, Heidelberg 1, Federal Republic of Germany

  Willi Jäger, Hermann Rost

• Institut für Dokumentation, Information und Statistik, Deutsches Krebsforschungszentrum, Heidelberg 1, Federal Republic of Germany

  Petre Tautu

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