Biological Growth and Spread: Mathematical Theories and Applications, Proceedings of a Conference Held at Heidelberg, July 16 – 21, 1979

Front Matter....Pages I-XI
Front Matter....Pages 1-2
Genetic Basis of Biological Growth....Pages 3-8
Some Observations on the Kinetics of Haehomoietic Stem Cells and their Relationship to the Spatial Cellular Organisation of the Tissue....Pages 9-22
Proliferative Cell Populations in Surface Epithelia: Biological Models for Cell Replacement....Pages 23-35
Density dependent Markov population processes....Pages 36-49
A Model of Development of a Cell....Pages 50-56
Spatial Spread in Branching Processes....Pages 57-67
Pattern Formation by Bacteria....Pages 68-81
Random processes in random environments....Pages 82-92
Segregation Model and its Applications....Pages 93-97
Positive Recurrence of Multi-Dimensional Population-Dependent Branching Processes....Pages 98-108
Population Growth with Large Random Fluctuations....Pages 109-118
Niche Overlap and Invasion of Competitors in Random Environments II. The Effects of Demographic Stochasticity....Pages 119-129
Behavior of Limiting Diffusions for Density-Dependent Branching processes....Pages 130-137
Front Matter....Pages 139-139
Local Interactions with a Global Signal: A Voter Model....Pages 141-144
Interacting Markov Processes....Pages 145-156
On a Class of Branching Processes on a Lattice with Interactions....Pages 157-164
The Asymptotic Behavior of a Probabilistic Model for Tumor Growth....Pages 166-172
An Ising Model of a Neural Network....Pages 173-179
Embryogenesis through Cellular Interactions....Pages 180-195
Biological Interpretation of a Random Configuration Model for Carcinogenesis....Pages 196-220
Front Matter....Pages 221-221
On the spatial spread of a pattern....Pages 223-232
Spatial Models in the Epidemiology of Infectious Diseases....Pages 233-261
Population Controlled Spread and Intensity of Diseases in Wildlife....Pages 262-266
Clines in a Discrete Time Model in Population Genetics....Pages 267-275
Clines Induced by Variable Migration....Pages 276-278
Asymptotic Behavior of the Solutions of the Fisher Equation....Pages 279-289
Random Walks and Probabilities of Genetic Identity in a Tree....Pages 290-295
Travelling-Front Solutions for Integrodifferential Equations II....Pages 296-309
Some Mathematical Considerations of How to Stop the Spatial Spread of a Rabies Epidemic....Pages 310-319
Some Deterministic Models for the Spread of Genetic and Other Alterations....Pages 320-349
Front Matter....Pages 351-352
Orientation of Cells Migrating in a Chemotactic Gradient....Pages 353-366
Theoretical Models for the Specific Adhesion of Cells to Cells or to Surfaces....Pages 367-376
Chemotaxis in Bacteria: A Beginner’s Guide to the Literature....Pages 377-378
Assessing the Keller-Segel Model: How Has It Fared?....Pages 379-387
Modeling Chemosensory Responses of Swimming Eukaryotes....Pages 388-396
Mathematical Model for Tissue Inflammation: Effects of Spatial Distribution, Cell Motility, and Chemotaxis....Pages 397-409
Mathematical Theories of Topotaxis....Pages 410-439
Front Matter....Pages 441-442
Connections between Stochastic and Ordinary Integral Equations....Pages 443-448
Relationships between stochastic and deterministic population models....Pages 449-467
Remarks on Limit Theorems for Partial Differential Equations with Random Coefficients....Pages 468-470
Front Matter....Pages 471-472
Topological Techniques in Reaction-Diffusion Equations....Pages 473-483
Percolation....Pages 484-494
Some Ergodic Theorems for Spatial Processes....Pages 495-503
Percolation Models in two and Three Dimensions....Pages 504-511
Back Matter....Pages 513-514