Mathematical Demography: Theory and Modeling, a recently released textbook by Arni S. R. Srinivasa Rao, is a comprehensive and rigorous treatment of population dynamics that bridges classical demography with modern mathematical and stochastic modeling and theory. This textbook is suitable for a one-semester course. It develops demographic models from first principles, integrating tools from differential equations and stochastic processes to provide a unified and deeply analytical framework.
Covering such topics as Euler–Lotka equations, two-population Lotka-Volterra models, three-population SIR models with their stability properties, life tables, PDE-based models, branching processes, and modern extensions involving machine learning, the text offers an unusually broad synthesis of deterministic and stochastic approaches. Recent advancements in the mathematical theory of stationary populations are included as a chapter. A distinguishing feature of the text is its step-by-step derivations and numerical examples, along with new formulations, extensions of classical results, and novel perspectives on population stability and replacement metrics.
Designed for advanced undergraduate students, graduate students, and researchers, the book balances mathematical rigor with pedagogical structure, offering detailed derivations, examples, and exercises, while maintaining a strong focus on theory. This text is positioned between theoretical demography and mathematical biology books. Students in actuarial sciences, demography, statistics, ecology, and applied mathematics would find the textbook a valuable reference for gaining a thorough command of modeling and theory.
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