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Increasingly, mathematical methods are being used to advantage in addressing the problems facing humanity in managing its environment. Problems in resource management and epidemiology especially have demonstrated the utility of quantitative modeling. To explore these approaches, the Center of Applied Mathematics at Cornell University organized a conference in Fall, 1987, with the objective of surveying and assessing the state of the art. This volume records the proceedings of that conference. Underlying virtually all of these studies are models of population growth, from individual cells to large vertebrates. Cell population growth presents the simplest of systems for study, and is of fundamental importance in its own right for a variety of medical and environmental applications. In Part I of this volume, Michael Shuler describes computer models of individual cells and cell populations, and Frank Hoppensteadt discusses the synchronization of bacterial culture growth. Together, these provide a valuable introduction to mathematical cell biology.
List of contents
I. Cell Population Dynamics.- Computer Models of Individual Living Cells in Cell Populations.- Synchronization of Bacterial Culture Growth.- II. Resource Management.- Biological Resource Modeling-A Brief Survey.- Mathematical Modeling in Plant Biology: Implications of Physiological Approaches for Resource Management.- Economics, Mathematical Models and Environmental Policy.- Stochastic Nonlinear Optimal Control of Populations: Computational Difficulties and Possible Solutions.- Optimal Evolution of Tree-Age Distribution for a Tree Farm.- III. Infectious Diseases.- Mathematical Models of Infectious Diseases in Multiple Populations.- Epidemic Models in Populations of Varying Size.- Stability and Thresholds in Some Age-Structured Epidemics.- Multiple Time Scales in the Dynamics of Infectious Diseases.- A Distributed-Delay Model for the Local Population Dynamics of a Parasitoid-Host System.- IV. Acquired Immunodefiency Syndrome (AIDS).- A Model for HIV Transmission and AIDS.- The Role of Long Periods of Infectiousness in the Dynamics of Acquired Immunodeficiency Syndrome (AIDS).- The Effect of Social Mixing Patterns on the Spread of AIDS.- Possible Demographic Consequences of HIV/AIDS Epidemics: II, Assuming HIV Infection Does Not Necessarily Lead to AIDS.- V. Fitting Models to Data.- Fitting Mathematical Models to Biological Data: A Review of Recent Developments.- Inverse Problems for Distributed Systems: Statistical Tests and Anova.- Small Models are Beautiful: Efficient Estimators are Even More Beautiful.- VI. Dynamic Properties of Population Models.- Inferring the Causes of Population Fluctuations.- Stochastic Growth Models: Recent Results and Open Problems.- Use Differential Geometry with the Secret Ingredient: Gradients!.- Obstacles to Modelling Large DynamicalSystems.
