Age-structured population dynamics in demography and epidemiology / Hisashi Inaba.
This book is the first one in which basic demographic models are rigorously formulated by using modern age-structured population dynamics, extended to study real-world population problems. Age structure is a crucial factor in understanding population phenomena, and the essential ideas in demography...
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| Format: | eBook |
| Language: | English Japanese |
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Singapore :
Springer,
[2017]
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Table of Contents:
- Preface; Acknowledgements; Contents; 1 The Stable Population Model; 1.1 Basic Model Ingredients; 1.1.1 Introduction; 1.1.2 Mortality; 1.1.3 Fertility; 1.1.4 Malthusian Populations; 1.2 Fundamental Theorem of Demography; 1.2.1 The Stable Population Model; 1.2.2 Classical Solutions; 1.2.3 Semigroup Solutions; 1.2.4 Generation Expansion and R0; 1.2.5 Fundamental Theorem of Demography; 1.2.6 The Intrinsic Rate of Natural Increase; 1.3 The Dual System and the Reproductive Value; 1.3.1 The Population Operator; 1.3.2 The Reproductive Value; 1.3.3 Fundamental Solutions.
- 1.3.4 Backward System and Demographic Potential1.3.5 Stochastic Interpretations; 1.4 Some Demographic Applications; 1.4.1 Demographic Indices; 1.4.2 The Population Momentum; 1.4.3 Preston
- Coale System; 1.4.4 Perturbation Theory; 1.5 Age Profile Dynamics of Quasi-stable Populations; References; 2 Extensions of the Linear Theory; 2.1 Multistate Stable Population Model; 2.2 Inhomogeneous Linear Problems; 2.2.1 Stable Population Model with Immigration; 2.2.2 Population Dynamics of Marine Invertebrates; 2.3 Linear Marriage Models; 2.3.1 First-Marriage Model.
- 2.3.2 Reproduction by Non-persistent Unions2.4 Parity Progression Model; 2.5 Growth and Diffusion in Continuous State Spaces; 2.5.1 McKendrick Equation with an Additional Structure; 2.5.2 Traveling Wave Solutions; 2.6 Ergodicity Theorems for Non-autonomous Systems; 2.6.1 Primary System and Ergodicity; 2.6.2 Dual System and Ergodicity; 2.6.3 Generalized Stable Populations; 2.6.4 Periodic Stable Populations; References; 3 Nonlinear One-Sex Models; 3.1 Period Control Model; 3.1.1 Basic Model and Its Well-Posedness; 3.1.2 Stationary Solutions and Their Stability; 3.1.3 Exchange of Stability.
- 3.2 Global Behavior: Illustrative Examples3.2.1 Existence of Periodic Solutions; 3.2.2 Separable Models; 3.3 Cohort Control Model; 3.3.1 Basic Model; 3.3.2 Easterlin Cycle; References; 4 Pair Formation Models; 4.1 The Two-Sex Problem in Demography; 4.2 Kendall's Marriage Model; 4.2.1 Basic Model and Its Preliminary Analysis; 4.2.2 Exponential Solutions; 4.2.3 Stability of the Homogeneous System; 4.3 Pair Formation Models with Age Structure; 4.4 Malthusian Growth via Pair Formation; 4.4.1 Intra-cohort Marriage Models; 4.4.2 Inter-cohort Marriage Models; 4.5 Semigroup Approach; References.
- 5 Basic Ideas in Epidemic Modeling5.1 The Early Kermack
- McKendrick Model; 5.1.1 Basic Model; 5.1.2 Threshold Theorem and the Final Size Equation; 5.2 Three Applications; 5.2.1 Transmission by Environmental Contamination; 5.2.2 Virus Dynamics; 5.2.3 Asymptomatic Transmission Model; 5.3 Infection-Age-Dependent Model; 5.3.1 Linear Invasion Phase and R0; 5.3.2 Asymptotic Behavior; 5.3.3 The Intensity of Epidemic and Its Lower Bound; 5.4 Pandemic Threshold Theorem; 5.4.1 Basic Model and R0; 5.4.2 The Initial Value Problem; 5.4.3 The Final Size Equation of the Limiting Epidemic.