Deterministic Aspects of Mathematical Demography

Mathematical Demography, the study of population and its analysis through mathematical models, has received increased interest in the mathematical com munity in recent years. It was not until the twentieth century, however, that the study of population, predominantly human population, achieved its math ematical character. The subject of mathematical demography can be viewed from either a deterministic viewpoint or from a stochastic viewpoint. For the sake of brevity, stochastic models are not included in this work. It is, therefore, my intention to consider only established deterministic models in this discussion, starting with the life table as the earliest model, to a generalized matrix model which is developed in this treatise. These deterministic models provide sufficient de velopment and conclusions to formulate sound mathematical population analy sis and estimates of population projections. It should be noted that although the subject of mathematical demography focuses on human populations, the development and results may be applied to any population as long as the preconditions that make the model valid are maintained. Information concerning mathematical demography is at best fragmented.

Inhalt

1. The Development of Mathematical Demography.- 1.1 Introduction.- 1.2 Demography Before the Eighteenth Century.- 1.3 The Life Table Definitions and Consequences.- 1.4 The Life Table Practical Considerations as a Population Model.- 1.5 Early Models of Population Projections.- 1.6 Mortality and Survival Revisited.- 1.7 Conclusion.- 1.8 Notes for Chapter One.- 2. An Overview of the Stable Theory of Population.- 2.1 Introduction.- 2.2 Duration of Events Compared to Time.- 2.3 Population Pyramids and Age-Specific Considerations.- 2.4 Classical Formulation of the Stable Theory of Population.- 2.5 An Overview of Deterministic Models in Stable Population Theory.- 2.6 Conclusion.- 2.7 Notes for Chapter Two.- 3. The Discrete Time Recurrence Model.- 3.1 Introduction.- 3.2 Linear Recurrence Equations A Pandect.- 3.3 The Discrete Time Recursive Stable Population Model.- 3.4 Conclusion.- 3.5 Notes for Chapter Three.- 4. The Continuous Time Model.- 4.1 Introduction.- 4.2 The Development of the Continuous Time Model.- 4.3 Solution of the Continuous Model According to Lotka.- 4.4 Considerations on the Continuous Model According to Feller.- 4.5 Asymptotic Considerations.- 4.6 Conclusion.- 4.7 Notes for Chapter Four.- 5. The Discrete Time Matrix Model.- 5.1 Introduction.- 5.2 Development of the Discrete Time Matrix Model.- 5.3 Population Stability and the Matrix Model.- 5.4 Stable Theory when the Eigenvalues are Distinct.- 5.5 Stable Theory with Eigenvalues Not all Distinct.- 5.6 Conclusion.- 5.7 Notes for Chapter Five.- 6. Comparative Aspects of Stable Population Models.- 6.1 Introduction.- 6.2 Similarities Among the Stable Models.- 6.3 Differences Among the Stable Models.- 6.4 Conclusion.- 6.5 Notes for Chapter Six.- 7. Extensions of Stable Population Theory.- 7.1Introduction.- 7.2 Some Parameters of Stable Population Theory.- 7.3 Some Fertility Measures in Stable Population Theory.- 7.4 Some Applications of Stable Population Theory.- 7.5 Perturbations of Stable Population Theory.- 7.6 Conclusion.- 7.7 Notes for Chapter Seven.- 8. The Kingdom of Denmark A Demographic Example.- 8.1 Introduction.- 8.2 A Chronological Summary of Demographic Data Retrieval in Denmark.- 8.3 Migration, Mortality and Fertility in Denmark.- 8.4 Conclusion.- 8.5 Notes for Chapter Eight.- The Continuous Time Model According to McKendrick von Foerster.- References.