This book is an outcome of the Second International Conference on Mathematical Population Dynamics. It is intended for mathematicians, statisticians, biologists, and medical researchers who are interested in recent advances in analyzing changes in populations of genes, cells, and tumors.
Table of Contents
Part I: Structured Populations 1. Analysis of a Cell Population Model with Unequal Division and Random Transition 2. Slow Oscillations in a Model of Cell Population Dynamics 3. Competing Size-Structured Species 4. Quiescence in Structured Population Dynamics: Applications to Tumor Growth 5. Altruistic Population Model with Sex Differences 6. Remarks on an Epidemic Model with Age Structure 7. Effect of Reducibility on the Deterministic Spread of Infection in a Heterogeneous Population 8. Analysis of Age-Structured Population Models with an Additional Structure 9. Mathematical Modeling of Cell Population Dynamics as Applied to the Study of Cellular Aging: A Review and Open Questions 10. What Can the Theory of Positive Operators Do for You? Part II: Ordinary and Partial Differential Equations Models 11. Population Models with State-Dependent Delays 12. Generalized Lyapunov Methods for Interactive Systems in Biology 13. Production, Development, and Maturation of Red Blood Cells: A Mathematical Model 14. The Effect of Rapid Oscillations in the Dynamics of Delay Equations 15. Controllability of Nonlinear Systems with Application to Analysis of Population Dynamics 16. Invariant Manifolds for Partial Functional Differential Equations 17. Competition in a Modified Gradostat 18. S-Domain Modeling of Neoplastic Cells Circulation in Mice 19. Generic Modeling of Population Dynamics with S-Systems: Exemplified with Even-Aged Stands of Loblolly Pine (Pinus taeda) Part III: AIDS and the Theory of Epidemics 20. Modeling Chagas’s Disease: Variable Population Size and Demographic Implications 21. Mixing Patterns in Models of AIDS 22. Impact of Sexual Behavior Structures on the Transmission Dynamics of HIV in Closed Homosexual Communities 23. Methods for Numerically Specifying a Dynamic Stochastic Model of an AIDS Epidemic in a Heterosexual Population 24. Stochastic Model for the AIDS Epidemic in a Homosexual Population 25. AIDS: Modeling the Mature Epidemic in the Gay Community Part IV: Stochastic Models 26. Screening for Cancer in Relation to the Natural History of the Disease 27. Distinguishing Between Single- and Multiple-Hazard Random Processes in Small Samples 28. Estimation of Growth and Metastatic Rates of Primary Breast Cancer 29. Dynamics of a Cellular Automaton with Randomly Distributed Elements 30. Stochastic Model to Explain the Biology and Epidemiology of the Ultraviolet Induction of Skin Cancer 31. Multiple-Pathway Model of Carcinogenesis Involving One- and Two-Stage Models 32. SIMEST: Technique for Model Aggregation with Considerations of Chaos 33. Statistical Modeling of T-Helper (T4) Cells: Application of Nonpara metric Density Estimation Part V: Cell Cycle Kinetics 34. Regularized Estimates of Cell Cycle Parameters in Populations Affected by Loss from Flow-Cytometry Data 35. Conjectures on the Mathematics of the Cell Cycle 36. Cell Size Control by Modulation of the Growth Rate of Individual Mammalian Cells 37. Evolution of Ideas about Bacterial Growth and Their Pertinence to Higher Cells 38. Simulation of Streptococcal Population Dynamics: Desynchronization and Balanced Size Distributions 39. Effects of the Variability of Cell Cycle Durations on Labeling Experiments 40. Two-Subcyclc Cell Cycle Model Part VI: Proliferation and Tumor Growth 41. Diffusion Models of Prevascular and Vascular Tumor Growth: A Review 42. Approaches to Modeling Kinetics of Colony-Forming Experiments 43. Application of a Three-Phase Growth Model Based on Stochastic Learning at the Cellular Level to Human Cancer Growth 44. Partial Hemopoietic Chimerism Described by Means of a Mathematical Model of the Erythroid Pathway 45. Simulation Studies on the Regrowth of Acute Myeloid Leukemia After Autologous Bone Marrow Transplantation Part VII: Genetics and Molecular Biology 46. Colony Size Heritability: A New Parameter for Characterizing Proliferating Populations of Normal and Tumor Cells 47. Effects of Selection and Mutations on the Probabilities of Identity between Genes in Small Populations 48. Comparison of Two Models for Initiation of Replication in Escherichia coli 49. Quantitative Shift Model and Generation of Single-Cell Heterogeneity
Ovide Arino is Professor of Mathematics at the University of Pau, France. The author or coauthor of nearly 50 articles, he is a member of the Society of Mathematical Biology. Dr. Arino received the B.S. (1971) degree from the University of Nice and Doctorate d’Etat (1980) degree from the University of Bordeaux I, both in France. David E. Axelrod is Associate Professor of Biological Sciences at the Waksman Institute, Rutgers University, Piscataway, New Jersey. The author or coauthor of nearly 80 journal articles, book chapters, and abstracts, he is a member of the Cell Kinetics Society, American Society for Cell Biology, American Society for Microbiology, and Genetics Society of America. Dr. Axelrod received the B.S. (1962) degree from the University of Chicago, Illinois, and Ph.D. (1967) degree from the University of Tennessee at Knoxville. Marek Kimmel is Associate Professor of Statistics at Rice University, Houston, Texas. The author or coauthor of over 50 journal articles and book reviews, he is a member of the Cell Kinetics Society, American Mathematical Society, and Institute of Mathematical Statistics. His principal interest is in the mathematics of populations. Dr. Kimmel received the M.S. (1977) and Ph.D. (1980) degrees from Silesian Technical University, Gliwice, Poland.