Series in Mathematical Biology and Medicine: Volume 6

Advances in Mathematical Population Dynamics — Molecules, Cells and Man

Proceedings of the 4th International Conference on Mathematical Population Dynamics

4th International Conference on Mathematical Population Dynamics

, Rice University, Houston, Texas, USA

, 23 – 27 May 1995

https://doi.org/10.1142/3511 | February 1998

Pages: 864

Edited by:
O Arino (Universite de Pau et des Pays de l’Adour, France),
D Axelrod (Rutgers University, USA), and
M Kimmel (Rice University, USA)

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ISBN: 978-981-4545-97-6 (ebook) USD 66.00 Add to cart

This is a collection of refereed papers presented at the 4th International Conference on Mathematical Population Dynamics. The selection of papers and their organization were made by the following persons: O Arino, D Axelrod, V Capasso, W Fitzgibbon, P Jagers, M Kimmel, D Kirschner, C Mode, B Novak, R Sachs, W Stephan, A Swierniak and H Thieme.

It features some of the new trends in cell and human population dynamics. The main link between the two traits is that human populations of concern here are essentially those subject to cell diseases, either the processes of anarchic proliferation or those by which some cell lines are killed by an infectious agent.

The volume is divided into 3 main parts. Each part is subdivided into chapters, each chapter concentrating on a specific aspect. Each aspect is illustrated by one or several examples, developed in sections contributed by several authors. A detailed introduction for each part will enable the reader to refer to chapters of interest. An index and a bibliography for each part is also included for easy reference.

This book will be useful for those interested in the subject matter.

Contents:

DNA, Viruses and Cells:
- At the Level of the Genome
- Models of Cell Population
- Estimations of Model Parameters
- Mathematical Analysis of Asynchronicity
- Effect of Radiation on Cells
Population Dynamics in Diseases in Man:
- Statistical AIDS Models
- Models with Threshold Behavior
- New Models of the AIDS Epidemic
- The Immune System
- Drug Side-Effects and Drug Resistance
- Mathematical Models for the Disease Dynamics of Tuberculosis
- Oligomerization and PrP^Sc Stability in Prion Propagation: A Mathematical Analysis
Further Mathematical Aspects:
- Semigroup Aspects
- Spatial Effects
- On Equilibria Convergence, Persistence and Attractiveness
- On Branching Processes
- Aspects of Controllability

Readership: Mathematicians and statisticians in cell/molecular biology, immunology, chemotherapy and epidemiology.

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Advances in Mathematical Population Dynamics — Molecules, Cells and Man: Proceedings of the 4th International Conference on Mathematical Population Dynamics

Pages:1–910

https://doi.org/10.1142/9789814529594

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The Table of Contents for the book is as follows:

Foreword
General presentation
PART I DNA, Viruses and Cells
- Chapter 1: At the level of the genome
  - Diploid sequence space, dominance, and evolution
  - Evolution of primate immunodeficiency viruses
  - Mathematical model of the hitchhiking effect, and its application to DNA polymorphism data
  - Computer simulation of expansions of CGG DNA triplet repeats in the fragile X syndrome
- Chapter 2: Models of cell population
  - Modeling a bistable trigger of mitosis
  - A purely deterministic model for the population dynamics of budding yeast
  - Unequal cell division in relation to mother cell size
  - Model of the dynamics of a branching system of the glial cell lineages in vitro
  - Coupling in branching - a tumour model with population size dependence
- Chapter 3: Estimations of model parameters
  - Nonlinear analysis of tumor cell population dynamics
  - Guarded weights of evidence and acceptability profiles for one-sided hypotheses using censored data
  - Estimation of cell cycle kinetic parameters by flow cytometry
  - Effect of cell loss on the estimation of potential doubling time of tumors using DNA-BrdUrd histograms
  - Estimation from degraded data in a compartmental model. A case-study
- Chapter 4: Mathematical analysis of asynchronicity
  - On the stable size distribution in a mathematical model for tumor cell growth reproducing by fission and the cellular resistance problem
  - Quiescence as an explanation for asynchronous exponential growth in a size structured cell population of exponentially growing cells. Part 1.
- Chapter 5: Effect of radiation on cells
  - Multistage models for radiation tumorigenesis in p53 deficient transgenic mice: computer simulation of the effect of single doses of radiation.
  - Radiation damage to a dynamic cell population
  - A stochastic model of carcinogenesis allowing for cell death
  - Modeling the survival of T-cell lymphocytes using branching processes with random number of ancestors
- Bibliography of Part I
PART II Population dynamics in diseases in Man
- Chapter 6: Statistical AIDS models
  - Model based back calculation for the HIV epidemic
  - The united states AIDS epidemic in first world context
- Chapter 7: Models with threshold behavior
  - Calculating R₀ for HIV infection via pair formation
  - Threshold parameters for stochastic heterosexual partnership models of HIV/AIDS formulated within multi type CMJ-processes
  - The threshold behaviour of stochastic epidemics
- Chapter 8: New models of the AIDS epidemic
  - A stochastic model for the HIV epidemic and effects of age and race on the HIV infection in homosexual populations
  - On fitting a nonlinear stochastic model accommodating heterogeneous risk behavior to public health data on a HIV/AIDS epidemic
  - Recruitment into a core group and its effect on the spread of a sexually transmitted disease
  - AIDS, behavioral choice, and the composition of the pool of available partners
  - Multistage models of HIV transmission among injecting drug users via shared injection equipment
- Chapter 9: The immune system
  - A mathematical model of a malaria vaccine with stage-specific effects
  - Host tolerance to antigenically varying parasites: A mathematical model
- Chapter 10: Drug side-effects and drug resistance
  - Optimal control of chemotherapy affecting the infectivity of HIV
  - Mathematical modelling of cancer chemotherapy: investigation of the resonance phenomenon
  - Optimal synchronization and recruitment protocols design via a gradient type method
  - Qualitative analysis of the infinite model for drug resistance evolution
  - Drug resistance in diffusive epidemic population models
- Chapter 11:
  - Mathematical models for the disease dynamics of tuberculosis
- Chapter 12:
  - Oligomerization and PrP^sc stability in prion propagation: A mathematical analysis
- Bibliography of Part II
PART III Further mathematical aspects
- Chapter 13: Semigroup aspects
  - Quasi-compact semigroups via bounded perturbation
- Chapter 14: Spatial effects
  - Well-posedness of a linear age-dependent population model with spatial distribution
  - Bounds on trajectories in diffusive predator-prey models
- Chapter 15: On equilibria, convergence, persistence and attractiveness
  - Recurrence of stochastic multipopulation models
  - Persistence and resilience in competitive systems
  - Are multiple endemic equilibria possible?
- Chapter 16: On branching processes
  - On the support and continuity of the limit distribution of a branching process in varying environments
  - A branching processes model for the balance between mutation and selection
- Chapter 17: Aspects of controllability
  - Controllability for partial functional differential equations
  - Null controllability of the population dynamics via controllers with “small” support
- Bibliography of Part III
Subject Index
Author Index