Contents. Part I Simple Single Species Models

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1 Prologue xvii Part I Simple Single Species Models 1 Continuous Population Models Exponential Growth The Logistic Population Model The Logistic Equation in Epidemiology Qualitative Analysis Harvesting in Population Models Constant-Yield Harvesting Constant-Effort Harvesting Eutrophication of a Lake: A Case Study Appendix: Parameters in Biological Systems Project: The Spruce Budworm Project: Estimating the Population of the United States Discrete Population Models Introduction: Linear Models Graphical Solution of Difference Equations Equilibrium Analysis Period-Doubling and Chaotic Behavior Discrete Time Metered Models A Two-Age Group Model and Delayed Recruitment Systems of Two Difference Equations Oscillation in Flour Beetle Populations: A Case Study Project: A Discrete SIS Epidemic Model Project: A Discrete-Time Two-Sex Pair-Formation Model xi

2 xii 3 Continuous Single-Species Population Models with Delays Introduction Models with Delay in Per Capita Growth Rates Delayed-Recruitment Models Models with Distributed Delay Harvesting in Delayed Recruitment Models Constant-Effort Harvesting Constant-Yield Harvesting Nicholson s Blowflies: A Case Study Project: A Model for Blood Cell Populations Project: Some Epidemic Models Project: A Neuron Interaction Model Part II Models for Interacting Species 4 Introduction and Mathematical Preliminaries The Lotka Volterra Equations The Chemostat Equilibria and Linearization Qualitative Behavior of Solutions of Linear Systems Periodic Solutions and Limit Cycles Appendix: Canonical Forms of 2 2 Matrices Project: A Model for Giving Up Smoking Project: A Model for Retraining of Workers by their Peers Project: A Continuous Two-Sex Population Model Continuous Models for Two Interacting Populations Species in Competition Predator Prey Systems Laboratory Populations: Two Case Studies Kolmogorov Models Mutualism The Spruce Budworm: A Case Study The Community Matrix The Nature of Interactions Between Species Invading Species and Coexistence Example: A Predator and Two Competing Prey Example: Two Predators Competing for Prey Project: A Simple Neuron Model Project: A Plant Herbivore Model

3 xiii 6 Harvesting in Two-species Models Harvesting of Species in Competition Harvesting of Predator Prey Systems Intermittent Harvesting of Predator Prey Systems Some Economic Aspects of Harvesting Optimization of Harvesting Returns Justification of the Optimization Result A Nonlinear Optimization Problem Economic Interpretation of the Maximum Principle Project: A Harvesting Model Project: Harvesting of Two Species Part III Structured Population Models 7 Models for Populations with Age Structure Linear Discrete Models Linear Continuous Models The Method of Characteristics Nonlinear Continuous Models Models with Discrete Age Groups Project: Ordinary Differential Equations with Age Structure Project: Nonlinear Age Structured Population Growth Project: A Size Structured Population Model Models for Populations with Spatial Structure Introduction Some Simple Examples of Metapopulation Models A General Metapopulation Model A Metapopulation Model with Residence and Travel The Diffusion Equation Solution by Separation of Variables Solutions in Unbounded Regions Linear Reaction Diffusion Equations Nonlinear Reaction Diffusion Equations Two-Species Interactions Diffusion in Two Dimensions Project: Cats and Birds in Space Project: The Cable Equation Project: Some Equations of Diffusion Type

4 xiv Part IV Disease Transmission Models 9 Epidemic Models Introduction to Epidemic Models The Simple Kermack McKendrick Epidemic Model A Branching-Process Disease-Outbreak Model Transmissibility Network and Compartmental Epidemic Models More Complicated Epidemic Models Exposed Periods Treatment Models An Influenza Model A Quarantine-Isolation Model An SIR Model with a General Infectious Period Distribution The Age of Infection Epidemic Model Models with Disease Deaths A Vaccination Model The Next Generation Matrix A Global Asymptotic Stability Result Directions for Generalization Some Warnings Project: Discrete Epidemic Models Project: Fitting Data for an Influenza Model Project: Social Interactions Models for Endemic Diseases A Model for Diseases with No Immunity The SIR Model with Births and Deaths Some Applications Herd Immunity Age at Infection The Interepidemic Period Epidemic Approach to Endemic Equilibrium The SIS Model with Births and Deaths Temporary Immunity Diseases as Population Control Parameter Estimation: Ordinary Least Squares Connecting Models to Data Ordinary Least Squares (OLS) Estimation Possible Extensions Project: Pulse Vaccination Project: A Model with Competing Disease Strains

5 xv Project: An Epidemic Model in Two Patches Project: Population Growth and Epidemics Project: Estimating Parameters for Leishmaniasis Project: Invasive Pneumococcal Disease Surveillance Data Epilogue References Index

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