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Princeton : Princeton University Press, c2003

xviii,543 s. : il. ; 24 cm

ISBN 0-691-09291-5 (brož.)

ISBN 0-691-09290-7 (váz.)

Princeton series in theoretical and computational biology

Obsahuje bibliografii na s. [519]-536 a rejstřík

Biologie populační - modelování matematické - studie

000058836

Preface xiii // Chapter 1. Some General Remarks on Mathematical Modeling 1 // Bibliographic Remarks 3 // PART 1. BASIC POPULATION GROWTH MODELS 5 // Chapter 2. Birth, Death, and Migration 7 // 2.1 The Fundamental Balance Equation of Population Dynamics 7 // 2.2 Birth Date Dependent Life Expectancies 9 // 2.3 The Probability of Lifetime Emigration 11 // Chapter 3. Unconstrained Population Growth for Single Species 13 // 3.1 Closed Populations 13 // 3.1.1 The Average Intrinsic Growth Rate for Periodic Environments 14 // 3.1.2 The Average Intrinsic Growth Rate for Nonperiodic Environments 17 // 3.2 Open Populations 19 // 3.2.1 Nonzero Average Intrinsic Growth Rate 21 // 3.2.2 Zero Average Intrinsic Growth Rate 28 // Chapter 4. Von Bertalanffy Growth of Body Size 33 // Chapter 5. Classic Models of Density-Dependent Population Growth for // Single Species 37 // 5.1 The Bernoulli and the Verhulst Equations 37 // 5.2 The Beverton-Holt and Smith Differential Equation 39 // 5.2.1 Derivation from a Resource-Consumer Model 40 // 5.2.2 Derivation from Cannibalism of Juveniles by Adults 42 // 5.3 The Ricker Differential Equation 45 // 5.4 The Gompertz Equation 47 // 5.5 A First Comparison of the Various Equations 47 // Chapter 6. Sigmoid Growth 51 // 6.1 General Conditions for Sigmoid Growth 52 // 6.2 Fitting Sigmoid Population Data 57 // Chapter 7. The Allee Effect // 7.1 First Model Derivation: Search for a Mate 65 // 7.2 Second Model Derivation: Impact of a Satiating Generalist Predator 67 // 7.3 Model Analysis 69 // Chapter 8. Nonautonomous Population Growth: Asymptotic Equality of Population Sizes 75 // Chapter 9. Discrete-Time Single-Species Models 81 // 9.1 The Discrete Analog of the Verhulst (Logistic) and the Bernoulli Equation: the Beverton-Holt Difference // Equation and Its Generalization 81 // 9.2 The Ricker Difference Equation 83 //

9.3 Some Analytic Results for Scalar Difference Equations 84 // 9.4 Some Remarks Concerning the Quadratic Difference Equation 99 // Bibliographic Remarks 104 // Chapter 10. Dynamics of an Aquatic Population Interacting with a Polluted Environment 107 // 10.1 Modeling Toxicant and Population Dynamics 108 // 10.2 Open Loop Toxicant Input 114 // 10.3 Feedback Loop Toxicant Input 117 // 10.4 Extinction and Persistence Equilibria and a // Threshold Condition for Population Extinction 120 // 10.5 Stability of Equilibria and Global Behavior of Solutions 125 // 10.6 Multiple Extinction Equilibria, Bistability and Periodic Oscillations 135 // 10.7 Linear Dose Response 139 // Bibliographic Remarks 149 // Chapter 11. Population Growth Under Basic Stage Structure 151 // 11.1 A Most Basic Stage-Structured Model 151 // 11.2 Well-Posedness and Dissipativity 153 // 11.3 Equilibria and Reproduction Ratios 155 // 11.4 Basic Reproduction Ratios and Threshold Conditions for Extinction versus Persistence 156 // 11.5 Weakly Density-Dependent Stage-Transition Rates and // Global Stability of Nontrivial Equilibria 157 // 11.6 The Number and Nature of Possible Multiple Nontrivial Equilibria 160 // 11.7 Strongly Density-Dependent Stage-Transition Rates and 162 // Periodic Oscillations // 11.8 An Example for Multiple Periodic Orbits and Both 166 // Supercritical and Subcriticai Hopf Bifurcation // 11.9 Multiple Interior Equilibria, Bistability, and Many Bifurcations for 168 // Pure Intrastage Competition // Bibliographic Remarks 181 // PART 2. STAGE TRANSITIONS AND DEMOGRAPHICS 183 // Chapter 12. The Transition Through a Stage 185 // 12.1 The Sojourn Function 185 // 12.2 Mean Sojourn Time, Expected Exit Age, and Expectation of Life 187 // 12.3 The Variance of the Sojourn Time, Moments and Central Moments 189 // 12.4 Remaining Sojourn Time and Its Expectation 190 //

12.5 Fixed Stage Durations 197 // 12.6 Per Capita Exit Rates (Mortality Rates) 199 // 12.7 Exponentially Distributed Stage Durations 201 // 12.8 Log-Normally Distributed Stage Durations 202 // 12.9 A Stochastic Interpretation of Stage Transition 206 // Bibliographic Remarks 209 // Chapter 13. Stage Dynamics with Given Input 211 // 13.1 Input and Stage-Age Density 211 // 13.2 The Partial Differential Equation Formulation 212 // 13.3 Stage Content and Average Stage Duration 217 // 13.4 Average Stage Age 219 // 13.5 Stage Exit Rates 221 // 13.5.1 The Fundamental Balance Equation of Stage Dynamics 222 // 13.5.2 Average Age at Stage Exit 224 // 13.6 Stage Outputs 226 // 13.7 Which Recruitment Curves Can Be Explained by Cannibalism of Newborns by Adults? 230 // Bibliographic Remarks 237 // Chapter 14. Demographics in an Unlimiting Constant Environment 239 // 14.1 The Renewal Equation 240 // 14.2 Balanced Exponential Growth 241 // 14.3 The Renewal Theorem: Approach to Balanced Exponential Growth 244 // Chapter 15. Some Demographic Lessons from Balanced Exponential Growth 255 // 15.1 Inequalities and Estimates for the Malthusian Parameter 255 // 15.2 Average Age and Average Age at Death in a Population at Balanced // Exponential Growth. Average Per Capita Death Rate 262 // 15.3 Ratio of Population Size and Birth Rate 266 // 15.4 Consequences of an Abrupt Shift in Maternity: // Momentum of Population Growth 267 // Bibliographic Remarks 270 // Chapter 16. Some Nonlinear Demographics 273 // 16.1 A Demographic Model with a Juvenile and an Adult Stage 274 // 16.2 A Differential Delay Equation 277 // Bibliographic Remarks 279 // PART 3. HOST-PARASITE POPULATION GROWTH: EPIDEMIOLOGY OF INFECTIOUS DISEASES // Chapter 17. Background // 17.1 Impact of Infectious Diseases in Past and Present Time // 17.2 Epidemiological Terms and Principles Bibliographic Remarks //

Chapter 18. The Simplified Kermack-McKendrick Epidemic Model // 18.1 A Model with Mass-Action Incidence // 18.2 Phase-Plane Analysis of the Model Equations. // The Epidemic Threshold Theorem // 18.3 The Final Size of the Epidemic. Alternative Formulation of the Threshold Theorem // Chapter 19. Generalization of the Mass-Action Law of Infection // 19.1 Population-Size Dependent Contact Rates // 19.2 Model Modification // 19.3 The Generafized Epidemic Threshold Theorem // Chapter 20. The Kermack-McKendrick Epidemic Model with Variable Infectivity // 20.1 A Stage-Age Structured Model // 20.2 Reduction to a Scalar Integral Equation Bibliographic Remarks // Chapter 21. SEIR (-? S) Type Endemic Models for “Childhood Diseases” // 21.1 The Model and Its Well-Posedness // 21.2 Equilibrium States and the Basic Replacement Ratio // 21.3 The Disease Dynamics in the Vicinities of // the Disease-Free and the Endemic Equilibrium: // Local Stability and the Interepidemic Period // 21.4 Some Global Results: Extinction, Persistence of the Disease; Conditions for Attraction to the Endemic Equilibrium Bibliographic Remarks // Chapter 22. Age-Structured Models for Endemic Diseases and Optimal Vaccination Strategies // 22.1 A Model with Chronological Age-Structure // 22.2 Disease-Free and Endemic Equilibrium: the Replacement Ratio // 22.3 The Net Replacement Ratio, and Disease Extinction and Persistence // 22.4 Cost of Vaccinations and Optimal Age Schedules // 22.5 Estimating the Net Replacement Ratio. // Susceptibility and Average Age at In ec ? // Optimal Vaccination Schedules Revisite Bibliographic Remarks // Chapter 23. Endemic Models with Multiple Groups or Populations // 23.1 The Model ... // 23.6 The Basic Replacement Ran... Special Raima of the Basic Replacement Matrix // 23.7 Some Special Cases of Mixing Bibliographic Remarks //

PART 4. TOOLBOX 419 // Appendix A Ordinary Differential Equations // A.1 Conservation of Positivity and Boun... // A.2 Planar Ordinary Differential Equation ys // A.3 The Method of Fluctuations A.4 Behavior in the Vicinity of an Equilibrium A.5 Elements of Persistence Theory Bibliographic Remarks Global Stability of a Compact Minimal Se // of Positive Matrices and Associated Linear // A.6 // A.7 Hopf Bifurcation // A. 8 Perron-Frobenius Theory // Dynamical Systems Bibliographic Remarks // Appendix ? Integration, Integral Equations, and Some Convex Analysis // B.1 The Stieltjes Integral of Regulated Functions // B.2 Some Elements from Measure Theory // B.3 Some Elements from Convex Analysis // B.4 Lebesgue-Stieltjes Integration B.5 Jensen’s Inequality and Related Materia // B.6 Volterra Integral Equations // B. 7 Critical and Regular Values of a Function // Bibliographic Remarks // Appendix C Some MAPLE Worksheets with Comments for Part 1 // C. 1 Fitting the Growth of in Closed Populations // C.2 Periodic Modulation of Expon (Figures 3.2 and 3.3) // C.3 Fitting Sigmoid Population-Growth Curves (Figures 6.1 and 6.2) 498 // C.4 Fitting Bernoulli’s Equation to Population Data of Sweden (Figure 6.3) 507 // C.5 Illustrating the Allee Effect (Figures 12-1 A) 510 // C.6 Dynamics of an Aquatic Population Interacting with a // Polluted Environment (Figure 10.3E) 513 // References 519 // Index 537