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.
General
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