Age-Structured Population Dynamics in Demography and Epidemiology

1. Front Matter

   Pages i-xix

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2. The Stable Population Model

   • Hisashi Inaba

   Pages 1-74

3. Extensions of the Linear Theory

   • Hisashi Inaba

   Pages 75-137

4. Nonlinear One-Sex Models

   • Hisashi Inaba

   Pages 139-179

5. Pair Formation Models

   • Hisashi Inaba

   Pages 181-218

6. Basic Ideas in Epidemic Modeling

   • Hisashi Inaba

   Pages 219-286

7. Age-Structured SIR Epidemic Model

   • Hisashi Inaba

   Pages 287-331

8. Epidemic Models for HIV Infection

   • Hisashi Inaba

   Pages 333-377

9. Variable Susceptibility, Reinfection, and Immunity

   • Hisashi Inaba

   Pages 379-442

10. Basic Reproduction Number \(R_0\)

    • Hisashi Inaba

    Pages 443-501

11. Mathematical Tools

    • Hisashi Inaba

    Pages 503-549

12. Back Matter

    Pages 551-555

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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 and epidemiology cannot be understood without mathematical formulation; therefore, this book gives readers a robust mathematical introduction to human population studies. In the first part of the volume, classical demographic models such as the stable population model and its linear extensions, density-dependent nonlinear models, and pair-formation models are formulated by the McKendrick partial differential equation and are analyzed from a dynamical system point of view. In the second part, mathematical models for infectious diseases spreading at the population level are examined by using nonlinear differential equations and a renewal equation. Since an epidemic can be seen as a nonlinear renewal process of an infected population, this book will provide a natural unification point of view for demography and epidemiology. The well-known epidemic threshold principle is formulated by the basic reproduction number, which is also a most important key index in demography. The author develops a universal theory of the basic reproduction number in heterogeneous environments. By introducing the host age structure, epidemic models are developed into more realistic demographic formulations, which are essentially needed to attack urgent epidemiological control problems in the real world.

• Age Structure
• Stable Population Model
• SIR Model
• Basic Reproduction Number
• Ergodic Theorems

“This well-written book is a recommendation for every researcher who is interested in a comprehensive and rigorous mathematical treatment of age-structured population dynamics.” (W. Huyer, Monatshefte für Mathematik, Vol. 192 (1), 2020)

• The University of Tokyo, Tokyo, Japan

  Hisashi Inaba

Hisashi Inaba, Professor, Graduate School of Mathematical Sciences, The University  of Tokyo, 3-8-1 Komaba Meguro-ku Tokyo 153-8914 Japan
inaba@ms.u-tokyo.ac.jp

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