Series Preface |
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v | |
Preface |
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vii | |
Acknowledgements |
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xi | |
Prologue |
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xvii | |
I Simple Single Species Models |
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1 | (124) |
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Continuous Population Models |
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3 | (48) |
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3 | (5) |
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The Logistic Population Model |
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8 | (5) |
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The Logistic Equation in Epidemiology |
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13 | (4) |
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17 | (11) |
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Harvesting in Population Models |
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28 | (4) |
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Constant Yield Harvesting |
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28 | (1) |
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Constant Effort Harvesting |
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29 | (3) |
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Eutrophication of a Lake: A Case Study |
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32 | (8) |
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Appendix: Parameters in Biological Systems |
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40 | (5) |
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45 | (3) |
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Estimating the Population of the U.S.A |
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48 | (3) |
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Discrete Population Models |
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51 | (44) |
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Introduction: Linear Models |
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51 | (4) |
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Graphical Solution of Difference Equations |
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55 | (3) |
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58 | (6) |
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Period-Doubling and Chaotic Behavior |
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64 | (7) |
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Discrete Time Metered Models |
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71 | (3) |
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A Two-Age Group Model and Delayed Recruitment |
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74 | (6) |
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Systems of Two Difference Equations |
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80 | (3) |
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Oscillation in Flour Beetle Populations: A Case Study |
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83 | (7) |
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A Discrete SIS Epidemic Model |
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90 | (2) |
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A Discrete Time Two-Sex Pair Formation Model |
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92 | (3) |
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Continuous Single-Species Population Models with Delays |
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95 | (30) |
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95 | (3) |
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Models with Delay in Per Capita Growth Rates |
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98 | (4) |
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Delayed Recruitment Models |
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102 | (7) |
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Models with Distributed Delay |
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109 | (4) |
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Harvesting in Delayed Recruitment Models |
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113 | (4) |
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Constant Effort Harvesting |
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113 | (1) |
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Constant Yield Harvesting |
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114 | (3) |
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Nicholson's Blowflies: A Case Study |
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117 | (4) |
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A Model for Blood Cell Populations |
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121 | (4) |
II Models for Interacting Species |
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125 | (148) |
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Introduction and Mathematical Preliminaries |
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127 | (44) |
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The Lotka-Volterra Equations |
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127 | (4) |
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131 | (1) |
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Equilibria and Linearization |
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132 | (9) |
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Qualitative Behavior of Solutions of Linear Systems |
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141 | (13) |
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Periodic Solutions and Limit Cycles |
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154 | (9) |
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Appendix: Canonical Forms of 2 x 2 Matrices |
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163 | (2) |
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A Model for Giving up Smoking |
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165 | (1) |
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A Model for Retraining of Workers by their Peers |
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166 | (1) |
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A Continuous Two-sex Population Model |
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167 | (4) |
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Continuous Models for Two Interacting Populations |
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171 | (60) |
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171 | (9) |
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180 | (12) |
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Laboratory Populations: Two Case Studies |
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192 | (4) |
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196 | (3) |
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199 | (7) |
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The Spruce Budworm: A Case Study |
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206 | (7) |
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213 | (4) |
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The Nature of Interactions Between Species |
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217 | (3) |
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Invading Species and Coexistence |
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220 | (2) |
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Example: A Predator and Two Competing Prey |
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222 | (4) |
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Example: Two Predators Competing for Prey |
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226 | (1) |
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227 | (4) |
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Harvesting in two-species models |
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231 | (42) |
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Harvesting of species in competition |
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231 | (6) |
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Harvesting of Predator-Prey Systems |
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237 | (9) |
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Intermittent Harvesting of Predator-Prey Systems |
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246 | (4) |
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Some Economic Aspects of Harvesting |
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250 | (6) |
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Optimization of Harvesting Returns |
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256 | (4) |
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Justification of the Optimization Result |
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260 | (3) |
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A Nonlinear Optimization Problem |
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263 | (6) |
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Economic Interpretation of the Maximum Principle |
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269 | (4) |
III Structured Populations Models |
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273 | (98) |
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Basic Ideas of Mathematical Epidemiology |
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275 | (64) |
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275 | (6) |
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281 | (7) |
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A Model for Diseases with No Immunity |
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288 | (4) |
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Models with Demographic Effects |
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292 | (10) |
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Disease as Population Control |
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302 | (7) |
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Infective Periods of Fixed Length |
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309 | (6) |
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A Model with a Fixed Period of Temporary Immunity |
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315 | (3) |
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Arbitrarily Distributed Infective Periods |
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318 | (3) |
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Directions for Generalization |
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321 | (5) |
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326 | (2) |
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A Model with Competing Disease Strains |
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328 | (3) |
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An Epidemic Model in Two Patches |
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331 | (1) |
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Population Growth and Epidemics |
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332 | (7) |
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Models for Populations with Age Structure |
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339 | (32) |
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339 | (7) |
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346 | (8) |
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Nonlinear Continuous Models |
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354 | (7) |
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Numerical Methods for the McKendrick-Von Foerster Model |
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361 | (10) |
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A Numerical Scheme for the McKendrick-Von Foerster Model |
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363 | (8) |
Epilogue |
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371 | (2) |
IV Appendix |
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373 | (14) |
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A Answered to Selected Exercises |
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375 | (12) |
References |
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387 | (22) |
Index |
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409 | |