Mathematical approaches to problems in resource management and epidemiology : proceedings of a conference held at Ithaca, N.Y., Oct. 28-30, 1987

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. Front Matter....Pages N2-VII Front Matter....Pages 1-1 Computer Models of Individual Living Cells in Cell Populations....Pages 2-15 Synchronization of Bacterial Culture Growth....Pages 16-22 Front Matter....Pages 23-23 Biological Resource Modeling—A Brief Survey....Pages 24-31 Mathematical Modeling in Plant Biology: Implications of Physiological Approaches for Resource Management....Pages 32-48 Economics, Mathematical Models and Environmental Policy....Pages 49-66 Stochastic Nonlinear Optimal Control of Populations: Computational Difficulties and Possible Solutions....Pages 67-81 Optimal Evolution of Tree-Age Distribution for a Tree Farm....Pages 82-99 Front Matter....Pages 101-101 Mathematical Models of Infectious Diseases in Multiple Populations....Pages 102-108 Epidemic Models in Populations of Varying Size....Pages 109-123 Stability and Thresholds in Some Age-Structured Epidemics....Pages 124-141 Multiple Time Scales in the Dynamics of Infectious Diseases....Pages 142-151 A Distributed-Delay Model for the Local Population Dynamics of a Parasitoid-Host System....Pages 152-162 Front Matter....Pages 163-163 A Model for HIV Transmission and AIDS....Pages 164-176 The Role of Long Periods of Infectiousness in the Dynamics of Acquired Immunodeficiency Syndrome (AIDS)....Pages 177-189 The Effect of Social Mixing Patterns on the Spread of AIDS....Pages 190-219 Possible Demographic Consequences of HIV/AIDS Epidemics: II, Assuming HIV Infection does not Necessarily Lead to AIDS....Pages 220-248 Front Matter....Pages 249-249 Fitting Mathematical Models to Biological Data: A Review of Recent Developments....Pages 250-261 Inverse Problems for Distributed Systems: Statistical Tests and ANOVA....Pages 262-273 Small Models are Beautiful: Efficient Estimators are Even More Beautiful....Pages 274-284 Front Matter....Pages 285-285 Inferring the Causes of Population Fluctuations....Pages 286-307 Front Matter....Pages 285-285 Stochastic Growth Models: Recent Results and Open Problems....Pages 308-312 Use Differential Geometry with the Secret Ingredient: Gradients!....Pages 313-318 Obstacles to Modelling Large Dynamical Systems....Pages 319-327 Erratum to: Mathematical Modeling in Plant Biology: Implications of Physiological Approaches for Resource Management....Pages 329-329 Erratum to: Economics, Mathematical Models and Environmental Policy....Pages 329-330 Back Matter....Pages 331-333 The Center for Applied Mathematics at Cornell University sponsored a Special Year on Resource Management and Environmental Problem Solving in 1987-88 culminating in a Symposium on Mathematical Approaches to Resource Management and Epidemiology (October 28-30, 1987), aimed at identifying critical problems and new directions demanding mathematical attention, in these areas. The contributions of the invited speakers, recorded in this volume, describe and analyze models in areas such as cell population growth, plant population dynamics, and the spread of AIDS. They also address methodological aspects, and theoretical and interdisciplinary issues including the interplay between population biology, management, and economics, and the relationship between models and data. Throughout authors review past contributions and point to new directions