An introduction to mathematical epidemiology:
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| Format: | Buch |
| Sprache: | English |
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New York
Springer
[2015]
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| Schriftenreihe: | Texts in applied mathematics
volume 61 |
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| Beschreibung: | xiv, 453 Seiten Illustrationen, Diagramme (teilweise farbig) |
| ISBN: | 9781489976116 9781489978325 |
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| 245 | 1 | 0 | |a An introduction to mathematical epidemiology |c Maia Martcheva |
| 264 | 1 | |a New York |b Springer |c [2015] | |
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| 300 | |a xiv, 453 Seiten |b Illustrationen, Diagramme (teilweise farbig) | ||
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| 490 | 1 | |a Texts in applied mathematics |v volume 61 | |
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Infectious diseases | |
| 650 | 4 | |a Microbiology | |
| 650 | 4 | |a Mathematical models | |
| 650 | 4 | |a Biomathematics | |
| 650 | 4 | |a Genetics and Population Dynamics | |
| 650 | 4 | |a Infectious Diseases | |
| 650 | 4 | |a Mathematical Modeling and Industrial Mathematics | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematisches Modell | |
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Datensatz im Suchindex
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| adam_text | Contents 1 Introduction..................................................................................................... 1.1 Epidemiology ........................................................................................ 1.2 Classification of Infectious Diseases.................................................... 1.3 Basic Definitions in the Epidemiology of Infectious Diseases.......... 1.4 Historical Remarks on Infectious Diseases and Their Modeling 1.5 General Approach to Modeling............................................................ 1 1 1 3 4 6 2 Introduction to Epidemic Modeling........................................................... 2.1 Kermack-McKendrick SIR Epidemic Model...................................... 2.1.1 Deriving the Kermack-McKendrick Epidemic Model.......... 2.1.2 Mathematical Properties of the SIR Model............................ 2.2 The Kermack-McKendrick Model: Estimating Parameters from Data......................................................................................................... 2.2.1 Estimating the Recovery Rate.................................................. 2.2.2 The SIR Model and Influenza at an English Boarding School 1978 .............................................................................. 2.3 A Simple SIS Epidemic Model............................................................. 2.3.1 Reducing the SIS Model to a Logistic Equation.................... 2.3.2 Qualitative Analysis of the Logistic Equation........ ................ 2.3.3 General Techniques for Local Analysis of Single-Equation
Models........................................................................................ 2.4 An SIS Epidemic Model with Saturating Treatment.......................... 2.4.1 Reducing the SIS Model with Saturating Treatment to a Single Equation................................................................. 2.4.2 Bistability................................................................................. Problems......................................................................................................... 9 9 9 12 3 15 15 17 18 19 21 23 25 26 28 29 The SIR Model with Demography: General Properties of Planar Systems................................................................................................... 33 3.1 Modeling Changing Populations.......................................................... 33 3.1.1 The Malthusian Model............................................................. 33 ix
Contents x 4 3.1.2 The Logistic Model as a Model of Population Growth........ 3.1.3 A Simplified Logistic Model................................................... 3.2 The SIR Model with Demography ..................................................... 3.3 Analysis of Two-Dimensional Systems ............................................. 3.3.1 Phase-Plane Analysis................................................................ 3.3.2 Linearization............................................................................. 3.3.3 Two-Dimensional Linear Systems......................................... 3.4 Analysis of the Dimensionless SIR Model......................................... 3.4.1 Local Stability of the Equilibria of the SIR Model............... 3.4.2 The Reproduction Number of the Disease ^o ...................... 3.4.3 Forward Bifurcation.................................................................. 3.5 Global Stability..................................................................................... 3.5.1 Global Stability of the Disease-Free Equilibrium.................. 3.5.2 Global Stability of the Endemic Equilibrium........................ 3.6 Oscillations in Epidemic Models......................................................... Problems.......................................................................................................... 35 36 37 39 40 44 45 48 48 50 51 52 52 53 56 63 Vector-Borne Diseases...................................................................................... 67 67 67 68 68 70 70 73 75 76 79 83 85 86 4.1 Vector-Borne
Diseases: An Introduction ............................................ 4.1.1 The Vectors................................................................................ 4.1.2 The Pathogen............................................................................ 4.1.3 Epidemiology of Vector-Borne Diseases................................ 4.2 Simple Models of Vector-Borne Diseases .......................................... 4.2.1 Deriving a Model of Vector-Borne Disease............................ 4.2.2 Reproduction Numbers, Equilibria, and Their Stability........ 4.3 Delay-Differential Equation Models of Vector-Borne Diseases........ 4.3.1 Reducing the Delay Model to a Single Equation.................. 4.3.2 Oscillations in Delay-Differential Equations.......................... 4.3.3 The Reproduction Number of the Model with Two Delays .. 4.4 A Vector-Borne Disease Model with TemporaryImmunity............... Problems.......................................................................................................... 5 Techniques for Computing Җ..................................................................... 91 Building Complex Epidemiological Models ...................................... 91 5.1.1 Stages Related to Disease Progression.................................... 91 5.1.2 Stages Related to Control Strategies ....................................... 94 5.1.3 Stages Related to Pathogen or Host Heterogeneity................ 97 5.2 Jacobian Approach for the Computation of ^o.................................. 98 5.2.1 Examples in Which the Jacobian Reduces to a2 x
2 Matrix . 99 5.2.2 Routh-Hurwitz Criteria in Higher Dimensions........................ 100 5.2.3 Failure of the Jacobian Approach............................................... 103 5.3 The Next-Generation Approach.............................................................104 5.3.1 Van den Driessche and Watmough Approach........................... 104 5.3.2 Examples....................................................................................... 108 5.3.3 The Castillo-Chavez, Feng, and Huang Approach................... 116 Problems........................................................................................................... 119 5.1
Contents xi 6 Fitting Models to Data................................................................................... 123 6.1 Introduction............................................................................................. 123 6.2 Fitting Epidemie Models to Data: Examples........................................125 6.2.1 Using Matlab to Fit Data for the English Boarding School.. 126 6.2.2 Fitting World HIV/AIDS Prevalence........................................130 6.3 Summary of Basic Steps.......................................................................... 133 6.4 Model Selection........................................................................................ 134 6.4.1 Akaike Information Criterion....................................................135 6.4.2 Example of Model Selection Using AIC...................................137 6.5 Exploring Sensitivity ............................................................................. 139 6.5.1 Sensitivity Analysis of a Dynamical System............................. 139 6.5.2 Sensitivity and Elasticity of Static Quantities........................... 142 Problems........................................................................................................... 144 7 Analysis of Complex ODE Epidemic Models: Global Stability............ 149 7.1 Introduction..............................................................................................149 7.2 Local Analysis of the SEIR Model........................................................ 150 7.3 Global Stability via Lyapunov
Functions.............................................. 153 7.3.1 Lyapunov-Kasovskii-LaSalle Stability Theorems................ 153 7.3.2 Global Stability of Equilibria of the SEIR Model..................... 154 7.4 Hopf Bifurcation in Higher Dimensions................................................ 158 7.5 Backward Bifurcation..............................................................................165 7.5.1 Example of Backward Bifurcation and Multiple Equilibria.. 165 7.5.2 Castillo-Chavez and Song Bifurcation Theorem....................... 173 Problems........................................................................................................... 176 8 Multistrain Disease Dynamics...................................................................... 183 8.1 Competitive Exclusion Principle............................................................ 183 8.1.1 A Two-Strain Epidemic SIR Model........................................... 183 8.1.2 The Strain-One- and Strain-Two-Dominance Equilibria and Their Stability..................................................................... 186 8.1.3 The Competitive Exclusion Principle......................................... 189 8.2 Multistrain Diseases: Mechanisms for Coexistence ............................ 190 8.2.1 Mutation...................................................................................... 191 8.2.2 Superinfection...............................................................................192 8.2.3
Coinfection...................................................................................194 8.2.4 Cross-Immunity........................................................................... 195 8.3 Analyzing Two-Strain Models with Coexistence: The Case of Superinfection............................................................................ 197 8.3.1 Existence and Stability of the Disease-Free and Two Dominance Equilibria................................................................197 8.3.2 Existence of the Coexistence Equilibrium................................ 202 8.3.3 Competitive Outcomes, Graphical Representation, and Simulations ......................................................................... 205
Contents xii Computing the Invasion Numbers Using the Next-Generation Approach............................................................................................ 207 8.4.1 General Description of the Method ....................................... 207 8.4.2 Example................................................................................... 210 Problems...................................................................................................... 212 8.4 Control Strategies...................................................................................... 215 9.1 Introduction........................................................................................ 215 9.2 Modeling Vaccination; Single-Strain Diseases................................... 216 9.2.1 A Model with Vaccinationat Recruitment............................... 217 9.2.2 A Model with Continuous Vaccination.................................. 217 9.3 Vaccination and Genetic Diversity of Microorganisms......................224 9.4 Modeling Quarantine and Isolation.................................................... 230 9.5 Optimal Control Strategies................................................................. 234 9.5.1 Basic Theory of Optimal Control...........................................235 9.5.2 Examples.................................................................................237 Appendix..................................................................................................... 242
Problems..................................................................................................... 244 9 10 Ecological Context of Epidemiology ...................................................... 249 10.1 Infectious Diseases in Animal Populations......................................... 249 10.2 Generalist Predator and Si-Type Disease in Prey............................... 251 10.2.1 Indiscriminate Predation........................................................ 252 10.2.2 Selective Predation................................................................. 253 10.3 Generalist Predator and SIR-Туре Disease in Prey............................ 254 10.3.1 Selective Predation................................................................. 255 10.3.2 Indiscriminate Predation........................................................ 257 10.4 Specialist Predator and SI Disease in Prey......................................... 258 10.4.1 Lotka-Volterra Predator-Prey Models................................... 259 10.4.2 Lotka-Volterra Model with SI Disease in Prey...................... 262 10.5 Competition of Species and Disease.................................................. 268 10.5.1 Lotka-Volterra Interspecific Competition Models............... 269 10.5.2 Disease in One of the Competing Species.............................. 273 Problems..................................................................................................... 276 11 Zoonotic Disease, Avian Influenza, and Nonautonomous Models........281 11.1
Introduction........................................................................................281 11.2 Modeling Avian Influenza................................................................. 282 11.2.1 Simple Bird-Human AvianInfluenza Model ......................... 282 11.2.2 Parameterizing the Simple AvianInfluenza Model................. 283 11.2.3 Evaluating Avian Influenza Control Strategies...................... 284 11.3 Seasonality in Avian Influenza Modeling.......................................... 286 11.3.1 An Avian Influenza Model with Seasonality.......................... 286 11.3.2 Tools For Nonautonomous Models......................................... 288
Contents xiii 11.3.3 Analyzing the Avian Influenza Model with Seasonality .... 291 11.3.4 The Nonautonomous Avian Influenza Model with v¿ = 0... 293 11.3.5 The Full Nonautonomous Avian Influenza Model................ 296 Appendix...........................................................................................................296 Problems...........................................................................................................299 12 Age-Structured Epidemic Models............................................................... 301 12.1 Introduction.............................................................................................301 12.2 Linear Age-Structured Population Model............................................. 301 12.2.1 Derivation of the Age-Structured Model................................. 302 12.2.2 Reformulation of the Model Through the Method of the Characteristics. The Renewal Equation............. 307 12.2.3 Separable Solutions. Asymptotic Behavior............................. 309 12.3 Age-Structured SIS Epidemic Models................................................. 312 12.3.1 Introduction of the SIR Age-Structured Epidemic Model ... 313 12.3.2 Equilibria and Reproduction Number ..................................... 315 12.3.3 Local Stability of the Disease-Free Equilibrium..................... 317 12.4 Numerical Methods for Age-Structured Models................................. 321 12.4.1 A Numerical Method for the McKendrick-von Foerster Model.............................................................. 321 12.4.2
Numerical Method for the Age-Structured SIR Model........ 324 Problems...........................................................................................................326 13 Class-Age Structured Epidemic Models..................................................... 331 13.1 Variability of Infectivity with Time-Since-Infection........................... 331 13.2 Time-Since-Infection Structured SIR Model....................................... 333 13.2.1 Derivation of the Time-Since-Infection Structured Model... 333 13.2.2 Equilibria and Reproduction Number of the Time-Since-Infection SIR Model....................... 337 13.2.3 Local Stability of Equilibria..................................................... 339 13.3 Influenza Model Structured with Time-Since-Recovery..................... 344 13.3.1 Equilibria of the Time-Since-Recovery Model........................344 13.3.2 Stability of Equilibria................................................................. 346 13.3.3 Numerical Method for the Time-Since-Recovery Model.... 351 Appendix...........................................................................................................355 Problems...........................................................................................................357 14 Immuno-Epidemiological Modeling........................................................... 361 14.1 Introduction to Immuno-Epidemiological Modeling........................... 361 14.2 Within-Host Modeling........................................................................... 362 14.2.1 Modeling
Replication of Intracellular Pathogens.................... 363 14.2.2 Modeling the Interaction of the Pathogen with the Immune System............................................... 365 14.2.3 Combining Intracellular Pathogen Replication and Immune Response................................................... 367
xiv Contents 14.3 Nested Immuno-Epidemiological Models ........................................ 368 14.3.1 Building a Nested Immuno-Epidemiological Model............369 14.3.2 Analysis of the Immuno-Epidemiological Model...................371 14.3.3 Dependence of Mj and Prevalence on Immunological Parameters................................................................... 374 14.3.4 Sensitivity and Elasticity of Җ) and Prevalence with Respect to Immunological Parameters .............. 377 14.4 A Nested Immuno-Epidemiological Model with Immune Response ....................................................................................379 Problems...................................................................................................... 383 15 Spatial Heterogeneity in Epidemiological Models................................ 387 15.1 Introduction........................................................................................ 387 15.2 Metapopulation Modeling of Epidemic Spread..................................388 15.2.1 Lagrangian Movement Epidemic Models.............................. 389 15.2.2 Eulerian Movement Epidemic Models................................... 391 15.3 Spatial Models with Diffusion............................................................ 392 15.3.1 Derivation of Reaction-Diffusion Equations.......................... 393 15.3.2 Equilibria and Their Local Stability....................................... 396 15.3.3 Traveling-Wave Solutions...................................................... 399 15.3.4 Turing
Instability................................................................... 405 Problems..................................................................................................... 411 16 Discrete Epidemic Models..................................................... 415 16.1 Single-Species Discrete Population Models....................................... 415 16.1.1 Simple Discrete Population Models....................................... 415 16.1.2 Analysis of Single-Species Discrete Models.......................... 418 16.2 Discrete Epidemic Models................................................................. 421 16.2.1 A Discrete SIS Epidemic Model.............................................421 16.2.2 Analysis of Multidimensional Discrete Models.................... 422 16.2.3 Analysis of the SIS Epidemic Model..................................... 424 16.3 Discrete SEIS Model...........................................................................427 16.4 Next-Generation Approach for Discrete Models............................... 431 16.4.1 Basic Theory...........................................................................431 16.4.2 Examples................................................................................ 432 Problems..................................................................................................... 437 References.......................................................................................................... 441
Index.................................................................................................................. 449
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| adam_txt |
Contents 1 Introduction. 1.1 Epidemiology . 1.2 Classification of Infectious Diseases. 1.3 Basic Definitions in the Epidemiology of Infectious Diseases. 1.4 Historical Remarks on Infectious Diseases and Their Modeling 1.5 General Approach to Modeling. 1 1 1 3 4 6 2 Introduction to Epidemic Modeling. 2.1 Kermack-McKendrick SIR Epidemic Model. 2.1.1 Deriving the Kermack-McKendrick Epidemic Model. 2.1.2 Mathematical Properties of the SIR Model. 2.2 The Kermack-McKendrick Model: Estimating Parameters from Data. 2.2.1 Estimating the Recovery Rate. 2.2.2 The SIR Model and Influenza at an English Boarding School 1978 . 2.3 A Simple SIS Epidemic Model. 2.3.1 Reducing the SIS Model to a Logistic Equation. 2.3.2 Qualitative Analysis of the Logistic Equation. . 2.3.3 General Techniques for Local Analysis of Single-Equation
Models. 2.4 An SIS Epidemic Model with Saturating Treatment. 2.4.1 Reducing the SIS Model with Saturating Treatment to a Single Equation. 2.4.2 Bistability. Problems. 9 9 9 12 3 15 15 17 18 19 21 23 25 26 28 29 The SIR Model with Demography: General Properties of Planar Systems. 33 3.1 Modeling Changing Populations. 33 3.1.1 The Malthusian Model. 33 ix
Contents x 4 3.1.2 The Logistic Model as a Model of Population Growth. 3.1.3 A Simplified Logistic Model. 3.2 The SIR Model with Demography . 3.3 Analysis of Two-Dimensional Systems . 3.3.1 Phase-Plane Analysis. 3.3.2 Linearization. 3.3.3 Two-Dimensional Linear Systems. 3.4 Analysis of the Dimensionless SIR Model. 3.4.1 Local Stability of the Equilibria of the SIR Model. 3.4.2 The Reproduction Number of the Disease ^o . 3.4.3 Forward Bifurcation. 3.5 Global Stability. 3.5.1 Global Stability of the Disease-Free Equilibrium. 3.5.2 Global Stability of the Endemic Equilibrium. 3.6 Oscillations in Epidemic Models. Problems. 35 36 37 39 40 44 45 48 48 50 51 52 52 53 56 63 Vector-Borne Diseases. 67 67 67 68 68 70 70 73 75 76 79 83 85 86 4.1 Vector-Borne
Diseases: An Introduction . 4.1.1 The Vectors. 4.1.2 The Pathogen. 4.1.3 Epidemiology of Vector-Borne Diseases. 4.2 Simple Models of Vector-Borne Diseases . 4.2.1 Deriving a Model of Vector-Borne Disease. 4.2.2 Reproduction Numbers, Equilibria, and Their Stability. 4.3 Delay-Differential Equation Models of Vector-Borne Diseases. 4.3.1 Reducing the Delay Model to a Single Equation. 4.3.2 Oscillations in Delay-Differential Equations. 4.3.3 The Reproduction Number of the Model with Two Delays . 4.4 A Vector-Borne Disease Model with TemporaryImmunity. Problems. 5 Techniques for Computing Җ. 91 Building Complex Epidemiological Models . 91 5.1.1 Stages Related to Disease Progression. 91 5.1.2 Stages Related to Control Strategies . 94 5.1.3 Stages Related to Pathogen or Host Heterogeneity. 97 5.2 Jacobian Approach for the Computation of ^o. 98 5.2.1 Examples in Which the Jacobian Reduces to a2 x
2 Matrix . 99 5.2.2 Routh-Hurwitz Criteria in Higher Dimensions. 100 5.2.3 Failure of the Jacobian Approach. 103 5.3 The Next-Generation Approach.104 5.3.1 Van den Driessche and Watmough Approach. 104 5.3.2 Examples. 108 5.3.3 The Castillo-Chavez, Feng, and Huang Approach. 116 Problems. 119 5.1
Contents xi 6 Fitting Models to Data. 123 6.1 Introduction. 123 6.2 Fitting Epidemie Models to Data: Examples.125 6.2.1 Using Matlab to Fit Data for the English Boarding School. 126 6.2.2 Fitting World HIV/AIDS Prevalence.130 6.3 Summary of Basic Steps. 133 6.4 Model Selection. 134 6.4.1 Akaike Information Criterion.135 6.4.2 Example of Model Selection Using AIC.137 6.5 Exploring Sensitivity . 139 6.5.1 Sensitivity Analysis of a Dynamical System. 139 6.5.2 Sensitivity and Elasticity of Static Quantities. 142 Problems. 144 7 Analysis of Complex ODE Epidemic Models: Global Stability. 149 7.1 Introduction.149 7.2 Local Analysis of the SEIR Model. 150 7.3 Global Stability via Lyapunov
Functions. 153 7.3.1 Lyapunov-Kasovskii-LaSalle Stability Theorems. 153 7.3.2 Global Stability of Equilibria of the SEIR Model. 154 7.4 Hopf Bifurcation in Higher Dimensions. 158 7.5 Backward Bifurcation.165 7.5.1 Example of Backward Bifurcation and Multiple Equilibria. 165 7.5.2 Castillo-Chavez and Song Bifurcation Theorem. 173 Problems. 176 8 Multistrain Disease Dynamics. 183 8.1 Competitive Exclusion Principle. 183 8.1.1 A Two-Strain Epidemic SIR Model. 183 8.1.2 The Strain-One- and Strain-Two-Dominance Equilibria and Their Stability. 186 8.1.3 The Competitive Exclusion Principle. 189 8.2 Multistrain Diseases: Mechanisms for Coexistence . 190 8.2.1 Mutation. 191 8.2.2 Superinfection.192 8.2.3
Coinfection.194 8.2.4 Cross-Immunity. 195 8.3 Analyzing Two-Strain Models with Coexistence: The Case of Superinfection. 197 8.3.1 Existence and Stability of the Disease-Free and Two Dominance Equilibria.197 8.3.2 Existence of the Coexistence Equilibrium. 202 8.3.3 Competitive Outcomes, Graphical Representation, and Simulations . 205
Contents xii Computing the Invasion Numbers Using the Next-Generation Approach. 207 8.4.1 General Description of the Method . 207 8.4.2 Example. 210 Problems. 212 8.4 Control Strategies. 215 9.1 Introduction. 215 9.2 Modeling Vaccination; Single-Strain Diseases. 216 9.2.1 A Model with Vaccinationat Recruitment. 217 9.2.2 A Model with Continuous Vaccination. 217 9.3 Vaccination and Genetic Diversity of Microorganisms.224 9.4 Modeling Quarantine and Isolation. 230 9.5 Optimal Control Strategies. 234 9.5.1 Basic Theory of Optimal Control.235 9.5.2 Examples.237 Appendix. 242
Problems. 244 9 10 Ecological Context of Epidemiology . 249 10.1 Infectious Diseases in Animal Populations. 249 10.2 Generalist Predator and Si-Type Disease in Prey. 251 10.2.1 Indiscriminate Predation. 252 10.2.2 Selective Predation. 253 10.3 Generalist Predator and SIR-Туре Disease in Prey. 254 10.3.1 Selective Predation. 255 10.3.2 Indiscriminate Predation. 257 10.4 Specialist Predator and SI Disease in Prey. 258 10.4.1 Lotka-Volterra Predator-Prey Models. 259 10.4.2 Lotka-Volterra Model with SI Disease in Prey. 262 10.5 Competition of Species and Disease. 268 10.5.1 Lotka-Volterra Interspecific Competition Models. 269 10.5.2 Disease in One of the Competing Species. 273 Problems. 276 11 Zoonotic Disease, Avian Influenza, and Nonautonomous Models.281 11.1
Introduction.281 11.2 Modeling Avian Influenza. 282 11.2.1 Simple Bird-Human AvianInfluenza Model . 282 11.2.2 Parameterizing the Simple AvianInfluenza Model. 283 11.2.3 Evaluating Avian Influenza Control Strategies. 284 11.3 Seasonality in Avian Influenza Modeling. 286 11.3.1 An Avian Influenza Model with Seasonality. 286 11.3.2 Tools For Nonautonomous Models. 288
Contents xiii 11.3.3 Analyzing the Avian Influenza Model with Seasonality . 291 11.3.4 The Nonautonomous Avian Influenza Model with v¿ = 0. 293 11.3.5 The Full Nonautonomous Avian Influenza Model. 296 Appendix.296 Problems.299 12 Age-Structured Epidemic Models. 301 12.1 Introduction.301 12.2 Linear Age-Structured Population Model. 301 12.2.1 Derivation of the Age-Structured Model. 302 12.2.2 Reformulation of the Model Through the Method of the Characteristics. The Renewal Equation. 307 12.2.3 Separable Solutions. Asymptotic Behavior. 309 12.3 Age-Structured SIS Epidemic Models. 312 12.3.1 Introduction of the SIR Age-Structured Epidemic Model . 313 12.3.2 Equilibria and Reproduction Number . 315 12.3.3 Local Stability of the Disease-Free Equilibrium. 317 12.4 Numerical Methods for Age-Structured Models. 321 12.4.1 A Numerical Method for the McKendrick-von Foerster Model. 321 12.4.2
Numerical Method for the Age-Structured SIR Model. 324 Problems.326 13 Class-Age Structured Epidemic Models. 331 13.1 Variability of Infectivity with Time-Since-Infection. 331 13.2 Time-Since-Infection Structured SIR Model. 333 13.2.1 Derivation of the Time-Since-Infection Structured Model. 333 13.2.2 Equilibria and Reproduction Number of the Time-Since-Infection SIR Model. 337 13.2.3 Local Stability of Equilibria. 339 13.3 Influenza Model Structured with Time-Since-Recovery. 344 13.3.1 Equilibria of the Time-Since-Recovery Model.344 13.3.2 Stability of Equilibria. 346 13.3.3 Numerical Method for the Time-Since-Recovery Model. 351 Appendix.355 Problems.357 14 Immuno-Epidemiological Modeling. 361 14.1 Introduction to Immuno-Epidemiological Modeling. 361 14.2 Within-Host Modeling. 362 14.2.1 Modeling
Replication of Intracellular Pathogens. 363 14.2.2 Modeling the Interaction of the Pathogen with the Immune System. 365 14.2.3 Combining Intracellular Pathogen Replication and Immune Response. 367
xiv Contents 14.3 Nested Immuno-Epidemiological Models . 368 14.3.1 Building a Nested Immuno-Epidemiological Model.369 14.3.2 Analysis of the Immuno-Epidemiological Model.371 14.3.3 Dependence of Mj and Prevalence on Immunological Parameters. 374 14.3.4 Sensitivity and Elasticity of Җ) and Prevalence with Respect to Immunological Parameters . 377 14.4 A Nested Immuno-Epidemiological Model with Immune Response .379 Problems. 383 15 Spatial Heterogeneity in Epidemiological Models. 387 15.1 Introduction. 387 15.2 Metapopulation Modeling of Epidemic Spread.388 15.2.1 Lagrangian Movement Epidemic Models. 389 15.2.2 Eulerian Movement Epidemic Models. 391 15.3 Spatial Models with Diffusion. 392 15.3.1 Derivation of Reaction-Diffusion Equations. 393 15.3.2 Equilibria and Their Local Stability. 396 15.3.3 Traveling-Wave Solutions. 399 15.3.4 Turing
Instability. 405 Problems. 411 16 Discrete Epidemic Models. 415 16.1 Single-Species Discrete Population Models. 415 16.1.1 Simple Discrete Population Models. 415 16.1.2 Analysis of Single-Species Discrete Models. 418 16.2 Discrete Epidemic Models. 421 16.2.1 A Discrete SIS Epidemic Model.421 16.2.2 Analysis of Multidimensional Discrete Models. 422 16.2.3 Analysis of the SIS Epidemic Model. 424 16.3 Discrete SEIS Model.427 16.4 Next-Generation Approach for Discrete Models. 431 16.4.1 Basic Theory.431 16.4.2 Examples. 432 Problems. 437 References. 441
Index. 449 |
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| author | Martcheva, Maia |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 577 - Ecology 576 - Genetics and evolution |
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| discipline | Allgemeine Naturwissenschaft Biologie Mathematik Wirtschaftswissenschaften Medizin |
| discipline_str_mv | Allgemeine Naturwissenschaft Biologie Mathematik Wirtschaftswissenschaften Medizin |
| format | Book |
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| genre | (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV046696987 |
| illustrated | Illustrated |
| index_date | 2024-07-03T14:26:55Z |
| indexdate | 2024-07-10T08:51:23Z |
| institution | BVB |
| isbn | 9781489976116 9781489978325 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032107620 |
| oclc_num | 934647894 |
| open_access_boolean | |
| owner | DE-11 DE-83 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-20 DE-355 DE-BY-UBR |
| owner_facet | DE-11 DE-83 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-20 DE-355 DE-BY-UBR |
| physical | xiv, 453 Seiten Illustrationen, Diagramme (teilweise farbig) |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Springer |
| record_format | marc |
| series | Texts in applied mathematics |
| series2 | Texts in applied mathematics |
| spelling | Martcheva, Maia Verfasser (DE-588)1214457592 aut An introduction to mathematical epidemiology Maia Martcheva New York Springer [2015] © 2015 xiv, 453 Seiten Illustrationen, Diagramme (teilweise farbig) txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics volume 61 Mathematics Infectious diseases Microbiology Mathematical models Biomathematics Genetics and Population Dynamics Infectious Diseases Mathematical Modeling and Industrial Mathematics Mathematik Mathematisches Modell Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Infektionskrankheit (DE-588)4026879-2 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Infektionskrankheit (DE-588)4026879-2 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4899-7612-3 Texts in applied mathematics volume 61 (DE-604)BV002476038 61 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032107620&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Martcheva, Maia An introduction to mathematical epidemiology Texts in applied mathematics Mathematics Infectious diseases Microbiology Mathematical models Biomathematics Genetics and Population Dynamics Infectious Diseases Mathematical Modeling and Industrial Mathematics Mathematik Mathematisches Modell Mathematisches Modell (DE-588)4114528-8 gnd Infektionskrankheit (DE-588)4026879-2 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4026879-2 (DE-588)4151278-9 |
| title | An introduction to mathematical epidemiology |
| title_auth | An introduction to mathematical epidemiology |
| title_exact_search | An introduction to mathematical epidemiology |
| title_exact_search_txtP | An introduction to mathematical epidemiology |
| title_full | An introduction to mathematical epidemiology Maia Martcheva |
| title_fullStr | An introduction to mathematical epidemiology Maia Martcheva |
| title_full_unstemmed | An introduction to mathematical epidemiology Maia Martcheva |
| title_short | An introduction to mathematical epidemiology |
| title_sort | an introduction to mathematical epidemiology |
| topic | Mathematics Infectious diseases Microbiology Mathematical models Biomathematics Genetics and Population Dynamics Infectious Diseases Mathematical Modeling and Industrial Mathematics Mathematik Mathematisches Modell Mathematisches Modell (DE-588)4114528-8 gnd Infektionskrankheit (DE-588)4026879-2 gnd |
| topic_facet | Mathematics Infectious diseases Microbiology Mathematical models Biomathematics Genetics and Population Dynamics Infectious Diseases Mathematical Modeling and Industrial Mathematics Mathematik Mathematisches Modell Infektionskrankheit Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032107620&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002476038 |
| work_keys_str_mv | AT martchevamaia anintroductiontomathematicalepidemiology |